George Grätzer

Q: What Schools Are Affiliated With George Grätzer

George Grätzer is affiliated with the following schools: University of Calgary, Eötvös Loránd University, University of Manitoba

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George Grätzer

Mathematics

#2767

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#4204

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Algebra

#44

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#78

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Measure Theory

#477

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#678

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Mathematics

George Grätzer's Degrees

PhD Mathematics Eötvös Loránd University

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According to Wikipedia, George A. Grätzer is a Hungarian-Canadian mathematician, specializing in lattice theory and universal algebra. He is known for his books on LaTeX and his proof with E. Tamás Schmidt of the Grätzer–Schmidt theorem.

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George Grätzer's Published Works

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Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

General Lattice Theory (1978) (2485)
Lattice Theory: Foundation (1971) (613)
Lattice Theory: First Concepts and Distributive Lattices (1971) (560)
On congruence lattices of lattices (1962) (144)
Characterizations of congruence lattices of abstract algebras (1963) (125)
The structure of pseudocomplemented distributive lattices. II. Congruence extension and amalgamation (1971) (86)
Ideals and congruence relations in lattices (1958) (79)
The Congruences of a Finite Lattice (2005) (79)
Standard ideals in lattices (1964) (74)
Two Mal'cev-type theorems in universal algebra (1970) (65)
ON THE ENDOMORPHISM SEMIGROUP (AND CATEGORY) OF BOUNDED LATTICES (1970) (63)
Lattice theory : special topics and applications (2014) (62)
Notes on planar semimodular lattices. IV. The size of a minimal congruence lattice representation with rectangular lattices (2010) (55)
Joint review of general lattice theory (second edition) and the congruences of a finite lattice: a proof-by picture approach (2007) (46)
On ideal theory for lattices (1958) (46)
On a problem of M. H. Stone (1957) (43)
A new look at the Jordan-Hölder theorem for semimodular lattices (2010) (40)
Planar Semimodular Lattices: Structure and Diagrams (2014) (40)
INJECTIVE AND PROJECTIVE STONE ALGEBRAS (1971) (39)
The amalgamation property in equational classes of modular lattices. (1973) (39)
Equational classes of lattices (1966) (37)
A note on planar semimodular lattices (2008) (37)
Boolean functions on distributive lattices (1964) (36)
Homomorphisms of Distributive Lattices as Restrictions of Congruences (1986) (36)
A nonassociative extension of the class of distributive lattices (1973) (33)
Identities for globals (complex algebras) of algebras (1988) (33)
A representation theorem for multi-algebras (1962) (32)
Notes on planar semimodular lattices. II. Congruences (2008) (32)
Congruence lattices of small planar lattices (1995) (32)
Notes on Planar Semimodular Lattices. VII. Resections of Planar Semimodular Lattices (2012) (31)
Planar Semimodular Lattices: Congruences (2014) (31)
A lattice construction and congruence-preserving extensions (1995) (30)
Congruence-preserving extensions of finite lattices to sectionally complemented lattices (1999) (30)
The structure of pseudocomplemented distributive lattices. III. Injective and absolute subretracts (1972) (29)
The structure of tensor products of semilattices with zero (1981) (29)
Composition of functions (1970) (29)
A generalization of Stone’s representation theorem for Boolean algebras (1963) (28)
Varieties of Lattices (2011) (27)
On complete congruence lattices of complete lattices (1991) (26)
Congruences in slim, planar, semimodular lattices: The Swing Lemma (2014) (26)
Proper Congruence-Preserving Extensions of Lattices (1999) (26)
Homomorphisms and principal congruences of bounded lattices I. Isotone maps of principal congruences (2016) (26)
On the lattice of subalgebras of a Boolean algebra (1972) (25)
On the construction of complemented lattices (1969) (25)
Free products of lattices (1970) (25)
A survey of some open problems on $p_n$-sequences and free spectra of algebras and varieties (1992) (23)
Boolean extensions and normal subdirect powers of finite universal algebras (1967) (23)
On a result of Gábor Czédli concerning congruence lattices of planar semimodular lattices (2014) (22)
Infinitary varieties of structures closed under the formation of complex structures (1984) (22)
A CORRECTION TO SMALL REPRESENTATIONS OF FINITE DISTRIBUTIVE LATTICES AS CONGRUENCE LATTICES (1995) (21)
Congruences of fork extensions of slim, planar, semimodular lattices (2016) (21)
On the lattice of all join-endomorphisms of a lattice (1958) (20)
An extension theorem for planar semimodular lattices (2013) (19)
Congruence structure of planar semimodular lattices: the General Swing Lemma (2018) (18)
On the number of polynomials of an idempotent algebra. II. (1970) (18)
Some examples of weakly associative lattices (1973) (18)
On Complete Congruence Lattices of Complete Modular Lattices (1991) (17)
Congruence lattices of planar lattices (1992) (17)
Two ProblemsThat Shaped a Century of Lattice Theory (2007) (17)
Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices (2020) (17)
Homomorphisms and principal congruences of bounded lattices. II. Sketching the proof for sublattices (2017) (17)
The Strong Independence Theorem for Automorphism Groups and Congruence Lattices of Arbitrary Lattices (2000) (17)
On the Family of Certain Subalgebras of a Universal Algebra (1965) (17)
The complete congruence lattice of a complete lattice (1990) (17)
Homomorphisms and principal congruences of bounded lattices. III. The Independence Theorem (2017) (17)
On congruence lattices of m-complete lattices (1992) (17)
Lattice tolerances and congruences (2011) (17)
Congruences of fork extensions of lattices (2013) (17)
Isotone Maps as Maps of Congruences I. Abstract Maps (1997) (16)
On idempotent, commutative, and nonassociative groupoids (1971) (16)
ON THE INDEPENDENCE THEOREM OF RELATED STRUCTURES FOR MODULAR (ARGUESIAN) LATTICES (2003) (15)
Notes on planar semimodular lattices. VI. On the structure theorem of planar semimodular lattices (2013) (15)
Products of lattice varieties (1985) (14)
Complete Congruence Lattices of Complete Distributive Lattices (1995) (14)
A survey of tensor products and related constructions in two lectures (2001) (14)
Congruence lattices of uniform lattices (2003) (13)
Isotone Maps as Maps of Congruences. II. Concrete Maps (2001) (13)
Congruence-preserving extensions of finite lattices to isoform lattices (2004) (13)
On the endomorphism semigroup of simple algebras (1967) (13)
Stone algebras form an equational class: (Remarks on Lattice Theory III) (1969) (13)
Partial and free weakly associative lattices (1976) (13)
Congruence representations of join-homomorphisms of distributive lattices: a short proof (1996) (13)
Homomorphisms of Distributive Lattices as Restrictions of Congruences. II. Planarity and Automorphisms (1994) (13)
On the number of polynomials of a universal algebra. II (1970) (13)
The variety generated by planar modular lattices (2010) (12)
On finite automorphism groups of simple Arguesian lattices (1999) (12)
Math into LATEX (2000) (12)
The M3[D] construction and n-modularity (1999) (12)
Some preliminary results on the set of principal congruences of a finite lattice (2017) (12)
Notes on tolerance relations of lattices (1990) (11)
Equationally compact semilattices (1969) (11)
The order of principal congruences of a bounded lattice (2013) (11)
A theorem on doubly transitive permutation groups with application to universal algebras (1964) (11)
Characterizations of relatively complemented distributive lattices (2022) (11)
Notes on sectionally complemented lattices. I (2005) (10)
On the Jordan-Dedekind chain condition (1957) (10)
TOLERANCES, COVERING SYSTEMS, AND THE AXIOM OF CHOICE (1989) (10)
A construction of semimodular lattices (1985) (10)
A technical lemma for congruences of finite lattices (2013) (10)
Strong amalgamation of distributive lattices (1990) (9)
Chain conditions in the distributive free product of lattices (1969) (9)
Congruences and prime-perspectivities in finite lattices (2013) (9)
CONGRUENCE-PRESERVING EXTENSIONS OF FINITE LATTICES TO SEMIMODULAR LATTICES (2000) (9)
Free Decompositions of a Lattice (1975) (9)
Notes on planar semimodular lattices. V. Cover-preserving embeddings of finite semimodular lattices into simple semimodular lattices (2010) (9)
Two notes on lattice-congruences (1958) (8)
Regular congruence-preserving extensions of lattices (2001) (8)
“Complete-simple” distributive lattices (1993) (8)
A normal form theorem for lattices completely generated by a subset (1977) (8)
On subalgebra lattices of universal algebras (1967) (8)
Lattice Tensor Products i. Coordinatization (2002) (8)
On a new notion of independence in universal algebras (1967) (8)
Congruence lattices of function lattices (1994) (7)
Notes on sectionally complemented lattices. III (2005) (7)
Isotone maps on lattices (2011) (7)
The equational class generated by weakly associative lattices with the unique bound property (1979) (7)
A PROPERTY OF TRANSFERABLE LATTICES (1974) (7)
L A T E X documents (2004) (7)
A new lattice construction (2005) (7)
On a result of Birkhoff (1995) (7)
The lattice of quasivarieties of lattices (1979) (7)
On the lattice of complete congruences of a complete lattice: on a result of K. Reuter and R. Wille (1991) (7)
On the spectra of classes of algebras (1967) (7)
A characterization of semilattices (1970) (7)
Pasting and modular lattices (1989) (7)
Chain conditions in free products of lattices with infinitary operations. (1979) (7)
Characterizing representability by principal congruences for finite distributive lattices with a join-irreducible unit element (2021) (6)
On isotone functions with the Substitution Property in distributive lattices (1995) (6)
The unique amalgamation property for lattices (1990) (6)
Multipasting of lattices (1993) (6)
Complete congruence lattices of join-infinite distributive lattices (1997) (6)
Corrections to: ``The unique amalgamation property for lattices'' [Ann.\ Univ.\ Sci.\ Budapest.\ Eötvös Sect.\ Math.\ \bf 33 (1990), 167--176 (1991); MR1139361 (92m:06015)] (1992) (6)
Notes on the set of principal congruences of a finite lattice. I. Some preliminary results (2017) (6)
Free products of hopfian lattices (1974) (6)
First steps in LaTeX (1999) (6)
On the Congruence Lattice of a Lattice (1990) (6)
Positive universal classes in locally finite varieties (2010) (6)
Finite lattices with isoform congruences (2003) (6)
An equational basis in four variables for the three-element tournament (1992) (6)
ANOTHER CONSTRUCTION OF COMPLETE-SIMPLE DISTRIBUTIVE LATTICES (1992) (6)
Uniform representations of congruence schemes. (1978) (6)
Algebraic lattices as congruence lattices: The m-complete case (1991) (6)
Representing congruence lattices of lattices with partial unary operations as congruence lattices of lattices. I. Interval equivalence (2003) (5)
The free $$ \mathfrak{m} $$ -lattice on the poset H (1984) (5)
Birkhoff's representation theorem is equivalent to the axiom of choice (1986) (5)
Notes on sectionally complemented lattices. II (2005) (5)
Congruence lattices ofp-algebras (1995) (5)
A reduced free product of lattices (1971) (5)
Notes on tolerance relations of lattices: A conjecture of R.N. McKenzie (1990) (5)
Representations of join-homomorphisms of distributive lattices with doubly $2$-distributive lattices (1998) (5)
TWO OBSERVATIONS ON THE CONGRUENCE EXTENSION PROPERTY (1972) (5)
A Lower Bound for Congruence Representations (1997) (4)
Lattice tensor products. III - Congruences (2003) (4)
Subdirectly irreducible modular lattices of width at most 4 (2007) (4)
A Technique to Generate -Ary Free Lattices from Finitary Ones (1985) (4)
A “lattice theoretic” proof of the independence of the automorphism group, the congruence lattice, and the subalgebra lattice of an infinitary algebra (1990) (4)
On the Concept of Congruence Relation in Partial Algebras. (1967) (4)
Congruence Representations of Join-homomorphisms of Finite Distributive Lattices: Size and Breadth (2000) (4)
Homomorphisms and principal congruences of bounded lattices. III. The Independence Theorem (2017) (4)
Symmetric difference in abelian groups. (1978) (4)
Embedding lattices into lattices of ideals. (1979) (4)
On the number of join-irreducibles in a congruence representation of a finite distributive lattice (2003) (4)
Two embedding theorems for lattices (1978) (4)
Agassiz sum of algebras (1974) (4)
On the congruence lattice of a Scott-domain (1993) (4)
Congruence lattices of p -algebras (1995) (3)
My collaboration with E. T. Schmidt spanning six decades (2018) (3)
The spectrum of a finite pseudocomplemented lattice (2009) (3)
The closed subalgebras of a topological algebra (1966) (3)
More Math Into LaTeX (2016) (3)
On the Existence of Free Structures over Universal Classes (1968) (3)
Freely adjoining a relative complement to a lattice (2005) (3)
Universal algebra and lattice theory: a story and three research problems (1984) (3)
Math into TeX (1993) (3)
Free products and reduced free products of lattices (1973) (3)
Freely adjoining a complement to a lattice (2006) (3)
Math into LATEX: An Introduction to LATEX and AMS-LATEX (1995) (3)
Congruences and Trajectories in Planar Semimodular Lattices (2014) (3)
A variety of lattices whose quasivarieties are varieties (1978) (3)
Homomorphisms and principal congruences of bounded lattices (2015) (3)
An associativity theorem for alternative rings (1959) (3)
Representing homomorphisms of congruence lattices as restrictions of congruences of isoform lattices (2009) (3)
On Polynomial Algebras and Free Algebras (1968) (3)
ON SECTIONALLY COMPLEMENTED LATTICES . II . GENERALIZING THE 1960 SECTIONAL COMPLEMENT WITH AN APPLICATION TO CONGRUENCE RESTRICTIONS (2005) (3)
Applying the Czédli-Schmidt Sequences to Congruence Properties of Planar Semimodular Lattices (2021) (3)
Lattice tensor products. II (2002) (2)
A note on a special type of fully invariant subgroups of Abelian groups (1961) (2)
Two More Topics on Congruence Lattices of Lattices (2014) (2)
What Is New in LATEX? IV. WYSIWYG LATEX (2011) (2)
On generating free products of lattices (1974) (2)
Some Combinatorial Aspects of Congruence Lattice Representations (1999) (2)
Notes on planar semimodular lattices IX C1-diagrams (2023) (2)
Sublattices and standard congruences (1999) (2)
Planar Semimodular Lattices (2016) (2)
ON THE COMPLETE CONGRUENCE LATTICE OF A COMPLETE LATTICE WITH AN APPLICATION TO UNIVERSAL ALGEBRA (1989) (2)
Notes on sectionally complemented lattices. IV How far does the Atom Lemma go? (2007) (2)
Free-lattice-like sublattices of free products of lattices (1974) (2)
CONGRUENCE LATTICES, AUTOMORPHISM GROUPS OF FINITE LATTICES AND PLANARITY (1989) (2)
Generalized congruences and products of lattice varieties (1990) (2)
When is the free product of lattices complete (1977) (2)
Congruences of fork extensions of slim semimodular lattices (2013) (2)
On a problem of L. Fuchs concerning universal subgroups and universal homomorphic images of abelian groups (1961) (2)
Algebraic lattices as congruence lattices. The $\germ m$-complete case (1995) (2)
Lattice tensor products. IV (2004) (2)
Atom-generated planar lattices (2020) (2)
Congruence Lattices 101 (1999) (2)
Subdirectly irreducible members of products of lattice varieties (1988) (1)
The Construction of Some Free m-Lattices on Posets (1984) (1)
Using the Swing Lemma and \E C1-diagrams for congruences of planar semimodular lattices (2023) (1)
General Lattice Theory: 1979 Problem Update (1980) (1)
Addendum to: ``The lattice variety $\bf D\circ \bf D$'' [Acta Sci.\ Math.\ (Szeged) \bf 51 (1987), no.\ 1-2, 73--80; MR0911559 (89f:06008)] (1988) (1)
Remembering Ervin Fried and Jiří Sichler (2016) (1)
Review: V. N. Saliĭ, Lattices with Unique Complements (1990) (1)
Appendix 5. Primality the influence of Boolean Algebras in Universal Algebra (2008) (1)
Classes of congruence lattices of filtral varieties (1984) (1)
The anatomy of an article (1999) (1)
Practical LaTeX (2014) (1)
On the endomorphism monoids of (uniquely) complemented lattices (2000) (1)
Congruences of fork extensions of slim, planar, semimodular lattices (2016) (1)
A note on coalitions (1995) (1)
On a special type of subdirectly irreducible lattice with an application to products of varieties (1980) (1)
Appendix 3. Congruence Varieties (2008) (1)
Congruences and trajectories in SPS lattices (2014) (1)
A NOTE ON ABSOLUTELY FREE ALGEBRAS (1967) (1)
Congruence-preserving extensions of congruence-finite lattices to isoform lattices (2009) (1)
Congruences of the fork extensions. I. The Congruence Extension Property (2013) (1)
AMS-LATEX documents (1996) (0)
AMS documents and packages (2004) (0)
Research notes on congruences of planar semimodular lattices. I (2013) (0)
Ideals and congruence relations in lattices. I, II (1957) (0)
Isotone maps on lattices (2012) (0)
An extension theorem for planar semimodular lattices (2014) (0)
NOTES ON PLANAR SEMIMODULAR LATTICES. X. TWO REMARKS ON SLIM RECTANGULAR LATTICES (2022) (0)
The Structure of AMS-LaTex (1993) (0)
The order of principal congruences of a bounded lattice (2013) (0)
Chapter 10 B IB T E X (2004) (0)
Review: Mario Petrich, Categories of algebraic systems, and Jonathan D. H. Smith, Mal′cev varieties (1978) (0)
On isotone maps on a countable lattice (1999) (0)
Representing finite distributive lattices as congruence lattices of lattices (2013) (0)
On semi-discrete lattices whose congruence relations form a Boolean algebra (1963) (0)
Book Review: Categories of algebraic systems (1978) (0)
Legacy document classes (2007) (0)
Appendix 7 The Independence Proof (2008) (0)
Appendix 4. Equational Logic by Walter Taylor (2008) (0)
Your first article and presentation (2007) (0)
A technical lemma for congruences of finite lattices (2014) (0)
What is new in LaTeX? VII. The STIX Math Symbols (2015) (0)
On slim rectangular lattices (2023) (0)
A short proof of the congruence representation theorem of rectangular lattices (2013) (0)
TEX, L A TEX, and the Internet (2004) (0)
Multi-algebras as tolerance quotients of algebras (2012) (0)
Congruences and prime-perspectivities in finite lattices (2015) (0)
Some results on congruences of planar semimodular lattices (2013) (0)
A gentle learning curve for L A T E X (2008) (0)
The Preamble and the Topmatter (1993) (0)
Which freely generated lattices contain F(3)? (2008) (0)
Formulas and user-defined commands (1999) (0)
Free $\mathfrak {m}$-products of lattices. II (1986) (0)
The lattice variety $\bf D\circ \bf D$ (1987) (0)
Standard L A TEX documents (2004) (0)
What Is New in LaTeX? V. LaTeX on an iPad. Foundation (2013) (0)
On coverings of universal algebras (1967) (0)
What is new in LATEX? VI. LATEX on iPad empire (2013) (0)
Prime Intervals and Congruences (2016) (0)
Multi-algebras as tolerance quotients of algebras (2013) (0)
The AMS article document class (2016) (0)
Elements of Model Theory (2008) (0)
Congruences and Ideals (1978) (0)
Elementary Properties of Algebraic Constructions (2008) (0)
Remembering Ervin Fried and Jiří Sichler (2016) (0)
HOMOMORPHISMSOF DISTRIBUTIVE LATTICES A.S RESTRICTIONS OF CONGRUENCES (1986) (0)
Notes on tolerances relations of lattices I (1987) (0)
Abbott J. C.. Semi-Boolean algebra. Matematički vesnik , vol. 4 (1967), pp. 177–198. (1972) (0)
Constructions of Algebras (2008) (0)
The PDF file format (2016) (0)
A brief response to J. A. Cohen's joint review (2008) (0)
The Dilworth Theorem (2016) (0)
Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices (2020) (0)
A Friendly Afterword to the Reader (2011) (0)
Standard LATEX document classes (1996) (0)
Modular and Semimodular Lattices (2011) (0)
And a few more things (2016) (0)
NEW NOTES ON PLANAR SEMIMODULAR LATTICES. I. TWO REMARKS ON SLIM RECTANGULAR LATTICES (2022) (0)
Some preliminary results on the set of principal congruences of a finite lattice (2018) (0)
Dedicated to Bjarni Jonsson on his 70th birthday (1994) (0)
Customizing L A TEX (2004) (0)
Appendix 6 Equational Compactness (2008) (0)
FREE nt-PRODUCTS OF LATTICES. 11* (1986) (0)
Math into Tex - a simple introduction to AMS-Latex (1993) (0)
Patch extensions and trajectory colorings of slim rectangular lattices (0)
Some Applications of the Swing Lemma (2016) (0)
Commands and environments (2016) (0)
Customizing AMS-LaTex (1993) (0)
Notes on Planar Semimodular Lattices. VII. Resections of Planar Semimodular Lattices (2012) (0)
Congruence structure of planar semimodular lattices: the General Swing Lemma (2018) (0)
Appendix 1. General Survey (2008) (0)
Multiline math displays (2016) (0)
Books in LATEX (2016) (0)
Universalis Finite lattices and congruences . A survey (2005) (0)
Appendix 2. The Problems (2008) (0)
Math into T E X: a simple introduction to AMS-L A T E X (1993) (0)
Train Your Brain: A Year's Worth of Puzzles (2011) (0)
The Body of the Article (1993) (0)
An AMS article (1999) (0)
The Congruence Lattice and the Automorphism Group (2016) (0)
My collaboration with E. T. Schmidt spanning six decades (2018) (0)
Subalgebras and Homomorphisms (2008) (0)
Homomorphisms and principal congruences of bounded lattices. II. Sketching the proof for sublattices (2017) (0)
Reflexive Abelian Groups and Measurable Cardinals and Full Mad Families Sh904 (0)
Typing Your First Article (1993) (0)
Books in review (1984) (0)
Afterword to the English Translation (2011) (0)
On congruence lattices of $\germ m$-complete lattices (1992) (0)
Free ${\germ m}$-products of lattices. I (1984) (0)
Notes on planar semimodular lattices. VI. On the structure theorem of planar semimodular lattices (2013) (0)
Congruences and prime-perspectivity in semimodular lattices (2013) (0)
The LaTeX Book: A Guide for Documentation and Presentation (2007) (0)
Books in L A T E X (2004) (0)
David Sachs. The lattice of subalgebras of a Boolean algebra. Canadian journal of mathematics , vol. 14 (1962), pp. 451–460. (1972) (0)
Congruences of the fork extensions. II. The congruence gamma (2013) (0)
Sectionally Complemented Lattices (2016) (0)
This issue of Algebra Universalis is dedicated to the memory of András Huhn (1986) (0)
Working with Latex (1999) (0)
Putting L A TEX on the Web (2004) (0)
The Congruence Extension Property for fork extensions (2013) (0)

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George Grätzer's Degrees

Why Is George Grätzer Influential?

George Grätzer's Published Works

Published Works

Other Resources About George Grätzer

What Schools Are Affiliated With George Grätzer?

George Grätzer's AcademicInfluence.com Rankings