George Bergman | Academic Influence

George Bergman's AcademicInfluence.com Rankings

George Bergman

Mathematics

#2657

World Rank

#4064

Historical Rank

#1033

USA Rank

Measure Theory

#1184

World Rank

#1509

Historical Rank

#429

USA Rank

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Mathematics

George Bergman's Degrees

PhD Mathematics University of Chicago
Bachelors Mathematics University of Chicago

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Why Is George Bergman Influential?

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According to Wikipedia, George Mark Bergman, born on 22 July 1943 in Brooklyn, New York, is an American mathematician. He attended Stuyvesant High School in New York City and received his Ph.D. from Harvard University in 1968, under the direction of John Tate. The year before he had been appointed Assistant Professor of mathematics at the University of California, Berkeley, where he has taught ever since, being promoted to Associate Professor in 1974 and to Professor in 1978.

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George Bergman's Published Works

Number of citations in a given year to any of this author's works

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

The diamond lemma for ring theory (1978) (1136)
Lectures on curves on an algebraic surface (1966) (928)
The logarithmic limit-set of an algebraic variety (1971) (180)
Coproducts and some universal ring constructions (1974) (161)
A FIXED-POINT THEOREM FOR INWARD AND OUTWARD MAPS (1968) (130)
Rings with Fixed-Point-Free Group Actions (1973) (107)
Generating Infinite Symmetric Groups (2004) (100)
Hereditary Commutative Rings and Centres of Hereditary Rings (1971) (98)
Modules over coproducts of rings (1974) (95)
Centralizers in free associative algebras (1969) (83)
Universal derivations and universal ring constructions (1978) (80)
An Invitation to General Algebra and Universal Constructions (2015) (77)
A Number System with an Irrational Base (1957) (74)
Cogroups and Co-rings in Categories of Associative Rings (1996) (70)
Right orderable groups that are not locally indicable. (1991) (69)
Subgroups close to normal subgroups (1989) (61)
Boolean Rings of Projection Maps (1972) (49)
Some examples in PI ring theory (1974) (47)
Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups (1999) (41)
Ordering coproducts of groups and semigroups (1990) (40)
Errata: “A ring primitive on the right but not on the left” (1964) (38)
On universal derivations (1975) (38)
Hyperidentities of groups and semigroups (1981) (36)
Actions of Boolean rings on sets (1991) (36)
Groups Acting on Hereditary Rings (1971) (35)
On Groups Acting on Locally Finite Graphs (1968) (33)
Rational relations and rational identities in division rings (1976) (33)
On the existence of subalgebras of direct products with prescribedd-fold projections (1977) (26)
Ranks of tensors and change of base field (1969) (26)
Closed subgroups of the infinite symmetric group (2004) (24)
Nakayama’s lemma for half-exact functors (1972) (22)
The Semigroup of Ideals of a Fir is (Usually) Free (1975) (22)
P. I. Degrees and prime ideals (1975) (21)
Von Neumann regular rings with tailor-made ideal lattices (1986) (21)
Specially ordered groups (1984) (19)
Homomorphisms on infinite direct product algebras, especially Lie algebras (2009) (18)
A weak Nullstellensatz for valuations (1971) (17)
The Centres of 2-Firs and Hereditary Rings (1971) (16)
Symmetric Elements in Free Powers of Rings (1969) (16)
An inner automorphism is only an inner automorphism, but an inner endomorphism can be something strange (2010) (15)
Zero-divisors in tensor products (1976) (13)
Embedding rings in completed graded rings 3. Algebras over general k (1983) (13)
Heat dissipation from lithium/silver vanadium oxide cells during storage and low-rate discharge (1987) (12)
The automorphism class group of the category of rings (1973) (12)
Two statements about infinite products that are not quite true (2005) (12)
ON DIAGRAM-CHASING IN DOUBLE COMPLEXES (2011) (12)
Embedding rings in completed graded rings 1. Triangular embeddings (1983) (11)
Partially ordered sets, and minimal systems of counterexamples (1994) (11)
Every module is an inverse limit of injectives (2011) (10)
Homomorphisms on infinite direct products of groups, rings and monoids (2014) (9)
FAMILIES OF ULTRAFILTERS, AND HOMOMORPHISMS ON INFINITE DIRECT PRODUCT ALGEBRAS (2013) (9)
Embedding rings in completed graded rings 2. Algebras over a field (1983) (9)
Arrays of prime ideals in commutative rings (2003) (9)
Infinite multiplication of ideals in ℵ0-hereditary rings (1973) (9)
HEREDITARILY AND COHEREDITARILY PROJECTIVE MODULES (1972) (9)
HSP ≠ SHPS for metabelian groups, and related results (1989) (8)
Constructing division rings as module-theoretic direct limits (2002) (8)
On lattices of convex sets in $${\mathbb{R}}^{n}$$ (2004) (8)
Gel'fand-Kirillov dimension can go up in extension modules (1981) (7)
Mapping radii of metric spaces (2007) (7)
Isotone maps on lattices (2011) (7)
Gel’fand-kirillov dimensions of factor rings (1988) (7)
Some results on embeddings of algebras, after de Bruijn and McKenzie (2006) (7)
Terms and cyclic permutations (1978) (7)
On the scarcity of contravariant left adjunctions (1987) (6)
Embedding rings in completed graded rings 4. Commutative algebras (1983) (6)
Some examples of non-compressible rings (1984) (6)
Homomorphic images of pro-nilpotent algebras (2009) (6)
Co-rectangular bands and cosheaves in categories of algebras (1991) (6)
Linear maps on kI, and homomorphic images of infinite direct product algebras (2009) (6)
Can one factor the classical adjoint of a generic matrix? (2003) (6)
Connected fields of arbitrary characteristic (1966) (5)
Commuting matrices, and modules over Artinian local rings (2013) (5)
A note on factorizations of finite groups (2020) (5)
ON MONOIDS, 2 -FIRS, AND SEMIFIRS (2014) (5)
Direct limits and fixed point sets (2003) (5)
Sfields finitely right-generated over subrings (1983) (5)
Voltage delay and complex impedance characteristics of a high-rate lithium/silvervanadium oxide multiplate battery (extended abstract) (1989) (5)
COLIMITS OF REPRESENTABLE ALGEBRA-VALUED FUNCTORS (2007) (4)
Hyperidentities of groups and semigroups (1981) (4)
On monoids, $$2$$2-firs, and semifirs (2013) (4)
Embedding arbitrary algebras in groups (1988) (4)
On coproducts in varieties, quasivarieties and prevarieties (2008) (4)
Identities of cofinal sublattices (1985) (4)
Some results on embeddings of algebras , after (2007) (4)
Transversals of families in complete lattices, and torsion in product modules (1987) (4)
Adjoining a universal inner inverse to a ring element (2015) (4)
Continuity of homomorphisms on pro-nilpotent algebras (2010) (3)
The index of a group in a semigroup. (1971) (3)
ON COMMON DIVISORS OF MULTINOMIAL COEFFICIENTS (2008) (3)
Strong inner inverses in endomorphism rings of vector spaces (2016) (3)
Simplicial complexes with lattice structures (2016) (3)
On Vaughan Pratt's crossword problem (2015) (2)
LINEAR ULTRAFILTERS (2007) (2)
On core quandles of groups (2020) (2)
The amalgamation basis of the category of compact groups (1987) (2)
Every finite semigroup is embeddable in a finite relatively free semigroup (2004) (2)
Infinite joins that are finitely join-irreducible (1990) (2)
A cofinal coloring theorem for partially ordered algebras (1985) (2)
Infinite groups arising from partial presentations of finite groups (1999) (2)
Bilinear maps on Artinian modules (2011) (2)
Closed subgroups of infinite symmetric groups (2004) (1)
Some Category-Theoretic Ideas in Algebra ( A Too-Brief Tour of Algebraic Structure , Monads , and the Adjoint Tower ) (2010) (1)
Infinite Galois theory , Stone spaces , and profinite groups (1997) (1)
Some questions for possible submission to the next Kourovka notebook (2019) (1)
Minimal faithful modules over Artinian rings (2013) (1)
MORE ABELIAN GROUPS WITH FREE DUALS (2011) (1)
On the growth of algebras with bialgebra action (1997) (1)
Which group algebras cannot be made zero by imposing a single non-monomial relation? (2019) (1)
Thoughts on Eggert's Conjecture (2012) (1)
Normalizers of Semifirs in Their Universal Fields (1987) (1)
Some results relevant to embeddability of rings (especially group algebras) in division rings (2018) (1)
On group topologies determined by families of sets (2013) (1)
On Lattices of Convex Sets in R (2008) (1)
On k-Subspaces of L-vector-spaces (1998) (1)
Ordered Sets, Induction, and the Axiom of Choice (2015) (1)
ADDENDA TO \ON COMMON DIVISORS OF MULTINOMIAL COEFFICIENTS" (2010) (1)
Algebra & Number Theory (2009) (0)
Representable functors on categories of Lie algebras (1996) (0)
Representable functors from rings to general groups and semigroups (1996) (0)
xnA IN NONASSOCIATIVE ALGEBRAS, AND BASE-CHANGE (2009) (0)
Review of coalgebras and representable functors (1996) (0)
Directions for further investigation (1996) (0)
Corrections for the article “on the general theory of quotient rings” by V. P. Elizarov (1972) (0)
A Cook’s Tour of Other Universal Constructions (2015) (0)
Representable functors on categories of commutative associative algebras (1996) (0)
Completeness results for metrized rings and lattices (2018) (0)
Submonoids of groups, and group-representability of restricted relation algebras (2018) (0)
Representable functors from algebras over a field to rings (1996) (0)
Isotone maps on lattices (2012) (0)
Some notes on sets , logic , and mathematical language (2008) (0)
Some embedding results for associative algebras. (2020) (0)
A Further Generalization of Neustadt's Law (1959) (0)
Paul Moritz Cohn. 8 January 1924 — 20 April 2006 (2014) (0)
A counterexample in differential algebra (1965) (0)
Weakening partial orderings to lattice and semilattice orderings (1986) (0)
On lattices and their ideal lattices, and posets and their ideal posets (2008) (0)
Disputed parentage : the story of the universe (1988) (0)
Se p 20 04 On lattices of convex sets in R (2021) (0)
Multilinear algebra of representable functors on (1996) (0)
' Cojaments , suggestions , and related referenoes » eloomedJ Subgroups close to normal subgroups (2005) (0)
INFINITE DIRECT PRODUCT ALGEBRAS (2012) (0)
Some results on counting linearizations of posets (2018) (0)
Submonoids of groups, and group-representability of restricted relation algebras (2017) (0)
Review: P. M. Cohn, Skew field constructions (1979) (0)
Representable functors from rings to abelian groups (1996) (0)
Digressions on semigroups, etc. (1996) (0)
Lattices, Closure Operators, and Galois Connections (2015) (0)
Tensor products of faithful modules (2016) (0)
Thoughts on Eggert's Conjecture HIS (2014) (0)
Comment on a New Look at an Old Problem (1960) (0)
Algebra and Coalgebra Objects in Categories, and Functors Having Adjoints (2015) (0)
Criteria for existence of semigroup homomorphisms and projective rank functions (2010) (0)
An elementary result on infinite and finite direct sums of modules (2022) (0)
Universal Constructions in Category-Theoretic Terms (2015) (0)
Making Some Things Precise (2015) (0)
A Type of Algebraic Structure Related to Sets of Intervals (2020) (0)
CORRIGENDUM Groups Acting on Hereditary Rings (1972) (0)
American Mathematical Society Edited by with the Cooperation of Index to Volume 15 [december Cohomology of Groups in Arbitrary Categories (0)
About the Course, and These Notes (2015) (0)
Representable functors from -rings to rings (1996) (0)
TEXed November 20, 2019 GROUPS AND FLIP-SETS (2019) (0)
be the ring of formal polynomials Eizo diYi (dIED, nonzero for only (2016) (0)
Varieties of Algebras (2015) (0)
Categories and Functors (2015) (0)
TEXed July 8, 2015 SIMPLICIAL COMPLEXES WITH LATTICE STRUCTURES (2015) (0)
Transformations and Optics (1961) (0)
On the growth of algebras with bialgebra action (1996) (0)
A ug 2 00 5 Direct limits and fixed point sets (2005) (0)
G R ] 2 7 M ay 2 00 5 Closed subgroups of the infinite symmetric group (2005) (0)

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