Claus Michael Ringel | Academic Influence

Claus Michael Ringel's AcademicInfluence.com Rankings

Claus Michael Ringel

Mathematics

#4469

World Rank

#6342

Historical Rank

Algebra

#95

World Rank

#159

Historical Rank

Measure Theory

#814

World Rank

#1079

Historical Rank

mathematics Degrees

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Mathematics

Claus Michael Ringel's Degrees

PhD Mathematics University of Bonn

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According to Wikipedia, Claus Michael Ringel is a German mathematician, specializing in algebra. Education and career Ringel studied mathematics, physics and philosophy beginning in 1964 at the Goethe University Frankfurt with the Diplom degree in mathematics in 1968. He received in 1969 from the Goethe University Frankfurt his doctorate under the supervision of Friedrich-Wilhelm Bauer with thesis Diagonalisierungspaare in der Homologischen Algebra . He then became a research assistant at the University of Tübingen and in 1971/72 an assistant professor at Carleton University . In 1972 he habilitated in Tübingen and became there a Universitätsdozent.

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Claus Michael Ringel'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

Tame Algebras and Integral Quadratic Forms (1985) (1517)
Indecomposable Representations of Graphs and Algebras (1976) (638)
Hall algebras and quantum groups (1990) (549)
Auslander-reiten sequences with few middle terms and applications to string algebrass (1987) (495)
The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences (1991) (400)
Representations of K-species and bimodules (1976) (315)
The module theoretical approach to quasi-hereditary algebras (1992) (268)
Quasi-hereditary algebras (1989) (257)
Vinberg’s characterization of dynkin diagrams using subadditive functions with application to DTr-periodic modules (1980) (189)
The indecomposable representations of the dihedral 2-groups (1975) (157)
PBW-bases of quantum groups. (1996) (154)
Infinite dimensional representations of finite dimensional hereditary algebras (1979) (142)
Representations of finite dimensional algebras and related topics in Lie theory and geometry (2004) (136)
QF-3 rings. (1975) (122)
Finite dimensional hereditary algebras of wild representation type (1978) (121)
The braid group action on the set of exceptional sequences of a hereditary artin algebra (1994) (112)
Hall polynomials for the representation-finite hereditary algebras (1990) (110)
Invariant subspaces of nilpotent linear operators, I (2006) (99)
The Composition Algebra of a Cyclic Quiver (1993) (98)
Exceptional modules are tree modules (1998) (97)
The representation type of local algebras (1975) (92)
The Auslander-Reiten translation in submodule categories (2005) (90)
On algebras of finite representation type (1975) (85)
The derived category of a tubular algebra (1986) (84)
The rational invariants of the tame quivers (1980) (83)
Hall algebras revisited (1992) (76)
The preprojective algebra of a modulated graph (1980) (76)
Diagrammatic methods in the representation theory of orders (1979) (74)
Representations of quivers over the algebra of dual numbers (2011) (74)
Submodule categories of wild representation type (2004) (72)
Tame algebras (on algorithms for solving vector space problems. II) (1980) (70)
THE REGULAR COMPONENTS OF THE AUSLANDER-REITEN QUIVER OF A TILTED ALGEBRA (1988) (65)
Report on the Brauer-Thrall conjectures: Rojter's theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I) (1980) (64)
Representations of graphs and algebras (1974) (63)
The Ziegler spectrum of a tame hereditary algebra (1998) (62)
Green's Theorem on Hall Algebras (2007) (61)
Every Semiprimary Ring is the Endomorphism Ring of a Projective Module Over a Quasi-Hereditary Ring (1989) (61)
Infinite Dimensional Representations of Canonical Algebras (2002) (59)
Some Algebraically Compact Modules. I (1995) (56)
Infinite Length Modules. Some Examples as Introduction (2000) (56)
From representations of quivers via Hall and Loewy algebras to quantum groups (1992) (56)
The spectral radius of the Coxeter transformations for a generalized Cartan matrix (1994) (53)
Representations of Algebras and Related Topics: Lie algebras (arising in representation theory) (1992) (52)
The repetitive algebra of a gentle algebra (1997) (51)
Construction of tilted algebras (1981) (51)
The Gabriel–Roiter measure (2005) (50)
The Δ-Filtered Modules Without Self-Extensions for the Auslander Algebra of k[T]/〈Tn〉 (1999) (50)
The Gorenstein projective modules for the Nakayama algebras. I (2012) (50)
Infinite length modules (2000) (49)
The Hall Algebra Approach to Quantum Groups (2005) (49)
A construction for quasi-hereditary algebras (1989) (47)
Binary polyhedral groups and Euclidean diagrams (1980) (47)
The canonical algebras (1990) (47)
Representations of Algebras: Representation theory of finite-dimensional algebras (1986) (42)
Eigenvalues of Coxeter transformations and the Gelfand-Kirillov dimension of the preprojective algebras (1981) (42)
The self-injective cluster-tilted algebras (2007) (35)
Handbook of Tilting Theory: Appendix: Some remarks concerning tilting modules and tilted algebras. Origin. Relevance. Future. (2007) (35)
Iyama’s finiteness theorem via strongly quasi-hereditary algebras (2009) (34)
Representation theory of finite groups and finite-dimensional algebras : proceedings of the conference at the University of Bielefeld from May 15-17, 1991, and 7 survey articles on topics of representation theory (1991) (33)
Foundation of the Representation Theory of Artin Algebras, Using the Gabriel-Roiter Measure (2005) (32)
The intersection property of amalgamations (1972) (30)
From submodule categories to preprojective algebras (2012) (30)
Directing projective modules (1993) (30)
The canonical algebras (with an appendix by W. Crawley-Boevey) (1990) (29)
The minimal representation-infinite algebras which are special biserial (2011) (28)
Integral quadratic forms (1984) (28)
Representation Theory of Finite-Dimensional Algebras (2005) (26)
Gorenstein-projective and semi-Gorenstein-projective modules (2018) (26)
Pathological Modules over Tame Rings (1976) (26)
Hereditary Artinian rings of finite representation type (1980) (25)
Auslander algebras as quasi-hereditary algebras (1989) (25)
The Catalan combinatorics of the hereditary artin algebras (2015) (25)
Some Remarks Concerning Tilting Modules and Tilted Algebras. Origin. Relevance. Future. (An appendix to the Handbook of Tilting Theory) (2006) (24)
The Auslander bijections: how morphisms are determined by modules (2013) (23)
Representation-finite tree algebras (1981) (23)
Computational methods for representations of groups and algebras : Euroconference in Essen (Germany), April 1-5, 1997 (1999) (22)
The category of good modules over a quasi-hereditary algebra has almost split sequences (1989) (22)
The representations of tame hereditary algebras (1978) (22)
The Number of Support-Tilting Modules for a Dynkin Algebra (2014) (21)
A class of balanced non-uniserial rings (1971) (21)
Cluster-concealed algebras (2009) (20)
Decomposition of modules over right uniserial rings (1972) (20)
Recent Advances in the Representation Theory of Finite Dimensional Algebras (1991) (20)
Morphisms determined by objects: The case of modules over artin algebras (2011) (19)
Bricks in hereditary length categories (1983) (18)
Normal forms of real matrices with respect to complex similarity (1977) (18)
Hereditary triangulated categories (2016) (17)
REFLECTION FUNCTORS FOR HEREDITARY ALGEBRAS (1980) (17)
Indecomposable representations of the Kronecker quivers (2010) (17)
The spectrum of a finite dimensional algebra (1979) (17)
The number of complete exceptional sequences for a Dynkin algebra (2013) (16)
EXCEPTIONAL OBJECTS IN HEREDITARY CATEGORIES (2009) (16)
EXCEPTIONAL OBJECTS IN HEREDITARY CATEGORIES (2009) (16)
Categorification of the Fibonacci numbers using representations of quivers (2011) (15)
The Theorem of Bo Chen and Hall Polynomials (2006) (15)
Real Subspaces of a Quaternion Vector Space (1978) (15)
Rings with the double centralizer property (1972) (15)
Towards an explicit description of the quantum group of type An (1993) (15)
Socle-determined categories of representations of Artinian hereditary tensor algebras (1980) (15)
Perfect elements in the free modular lattices (1980) (14)
On the representation dimension of artin algebras (2011) (14)
Artin algebras of dominant dimension at least 2 (2007) (13)
Quiver Grassmannians for wild acyclic quivers (2017) (13)
Filtrations of right ideals related to projectivity of left ideals (1989) (13)
The Structure of Balanced Rings (1973) (13)
On generic modules for string algebras (2001) (12)
Kawada's theorem (1981) (12)
Separating tubular series (1983) (11)
The (n-1)-antichains in a root poset of width n (2013) (11)
Identities in Categories (1972) (11)
Algebraically Compact Modules Arising from Tubular Families. A Survey. (2002) (10)
Representation theory of Dynkin quivers. Three contributions (2016) (10)
Quiver Grassmannians and Auslander varieties for wild algebras (2013) (10)
Tame Algebras Are Wild (2007) (9)
Tame Algebras Are Wild (2007) (9)
SOCLE CONDITIONS FOR QF 1 RINGS (1973) (9)
Gorenstein-projective and semi-Gorenstein-projective modules. II (2019) (9)
The Representation Type of the Full Transforamtion Semigroup T4 (2000) (9)
The finitistic dimension of a Nakayama algebra (2020) (9)
Monofunctors as reflectors (1971) (9)
A bypass of an arrow is sectional (1992) (8)
Minimal infinite submodule-closed subcategories (2010) (8)
Gorenstein‐projective modules over short local algebras (2019) (8)
Cluster-additive functions on stable translation quivers (2011) (7)
The dimension of a quasi-hereditary algebra (1990) (7)
The First Brauer-Thrall Conjecture (2007) (7)
A module theoretical interpretation of properties of the root systems (1979) (7)
Unions of chains of indecomposable modules (1975) (7)
Modules of bounded length in Auslander-Reiten components (1988) (7)
Canonical forms of pairs of complex matrices (1991) (7)
Objective triangle functors (2014) (7)
The Fibonacci partition triangles (2011) (6)
LATTICE STRUCTURE OF TORSION CLASSES FOR HEREDITARY ARTIN ALGEBRAS (2014) (6)
A class of bounded hereditary noetherian domains (1985) (6)
The eigenvector variety of a matrix pencil (2017) (6)
THE GLOBAL DIMENSION OF THE ENDOMORPHISM RING OF A GENERATOR-COGENERATOR FOR A HEREDITARY ARTIN ALGEBRA (2008) (6)
Gabriel–Roiter inclusions and Auslander–Reiten theory (2009) (6)
THE GLOBAL DIMENSION OF THE ENDOMORPHISM RING OF A GENERATOR-COGENERATOR FOR A HEREDITARY ARTIN ALGEBRA (2008) (6)
Quantum Serre Relations (2001) (5)
Kronecker modules generated by modules of length 2 (2016) (5)
Lectures on Rings and Modules (1972) (5)
REPRESENTATION THEORY OF ALGEBRAS I: MODULES (2008) (5)
A construction of endofinite modules (2019) (5)
Towers of semi-simple algebras (1991) (5)
The Liu-schulz Example (2007) (5)
On radical square zero rings (2011) (5)
Lectures on QF-3 and QF-1 rings (1972) (5)
Representation Theory: Four papers on problems in linear algebra (1982) (4)
A remark on normal forms of matrices (1980) (4)
Algebras whose Auslander-Reiten quivers have large regular components (1992) (4)
The root posets and their rich antichains (2013) (4)
The Multisegment Duality and the Preprojective Algebras of Type A (1999) (4)
Krull–Remak–Schmidt Fails for Artinian Modules over Local Rings (2001) (4)
Distinguished Bases of Exceptional Modules (2012) (4)
Indecomposables live in all smaller lengths (2009) (4)
The elementary 3-Kronecker modules (2016) (4)
Commutative QF-1 rings (1974) (4)
Remarks on a paper by Skornyakov concerning rings for which every module is a direct sum of left ideals (1978) (4)
On Modules M such that both M and M∗ are Semi-Gorenstein-Projective (2020) (4)
Algebra at the Turn of the Century (2001) (3)
Indecomposable representations of orders and Dynkin diagramm (1979) (3)
The Ingalls-Thomas Bijections (2015) (3)
The Relevance and the Ubiquity of Prüfer Modules (2007) (3)
The Ladder Construction of Prüfer Modules (2007) (3)
Representation Theory and Algebraic Geometry: The Development of the Representation Theory of Finite Dimensional Algebras 1968 – 1975 (1997) (3)
The Hochschild cocycle corresponding to a long exact sequence (1990) (2)
Balanced local rings with commutative residue fields (1972) (2)
Koszul modules (and the $\Omega$-growth of modules) over short local algebras (2019) (2)
Realizations of Frobenius Functions (1998) (2)
On modular representations of A4 (1989) (2)
Whitehead ’ s Theory of Extension in Process and Reality (2007) (2)
Wild Algebras: Two Examples (2013) (2)
Commutative -1 rings (1974) (2)
A Construction of Endoonite Modules (1995) (2)
The representations of quivers of type A_n. A fast approach (2013) (2)
Indecomposable representations of finite-dimensional algebras (1983) (1)
Algebras, rings and their representations : proceedings of the international conference on Algebras, Modules and Rings, Lisbon, Portugal, 14-18 July 2003 (2006) (1)
Simple reflexive modules over finite-dimensional algebras (2020) (1)
The real root modules for some quivers. (2006) (1)
Linear Nakayama algebras which are higher Auslander algebras (2021) (1)
Static Subcategories of the Module Category of a Finite-Dimensional Hereditary Algebra (2014) (1)
Quasi-hereditary algebras and the geometry of representations of algebras (2018) (1)
The shift orbits of the graded Kronecker modules (2017) (1)
An introduction to the representation dimension of artin algebras (2008) (1)
Bautista and the Development of the Representation Theory or Artin Algebras (1)
DOMESTIC CANONICAL ALGEBRAS AND SIMPLE LIE ALGEBRAS (2017) (0)
Infinite Dimensional Representations of (2006) (0)
Representation theory of Dynkin quivers. Three contributions (2016) (0)
Construction of stable separating tubular families (1984) (0)
The short local algebras of dimension 6 with non-projective reflexive modules (2022) (0)
A construction of rings whose injective hulls allow a ring structure (1973) (0)
Tilting functors and tubular extensions (Notation, results, some proofs) (1984) (0)
On Modules M such that both M and M∗ are Semi-Gorenstein-Projective (2020) (0)
On modules M such that M and M* are semi-Gorenstein-projective (2020) (0)
SOME ALGEBRAICALLY COMPACT MODULES. I CLAUS (2011) (0)
The Ladder Construction of Pruefer Modules (2007) (0)
QF-1 rings of global dimension less than or = 2 (1973) (0)
Objective triangle functors (2014) (0)
Quivers, module categories, subspace categories (Notation, results, some proofs) (1984) (0)
QF - 1 Rings of Global Dimension ≦ 2 (1973) (0)
ReprÃ©sentations des graphes valuÃ©s (2018) (0)
R T ] 4 D ec 2 01 9 Gorenstein-projective modules over short local algebras (2019) (0)
Decision problems in finitely presented groups (1999) (0)
Cluster-additive functions on stable translation quivers (2012) (0)
The shift orbits of the graded Kronecker modules (2018) (0)
Exceptional representations of quivers (2013) (0)
From submodule categories to preprojective algebras (2014) (0)
Extension in PR Part IV (2008) (0)
G. Lusztig: Introduction to Quantum Groups [Book review] (1994) (0)
Generic Representations of Wild Quivers (2013) (0)
Some Auslander-Reiten quilts (2011) (0)
The --ltered Modules without Self-extensions for the Auslander Algebra of Kt]=ht N I (2007) (0)
Free submodules of indecomposable modules (2004) (0)
The category of good modules over a quasi-hereditary algebra. On contravariantly finite subcategories (1990) (0)
Are Special Biserial Algebras Homologically Tame? (2021) (0)
Book Review: Representation theory of Artin algebras (1996) (0)
Dieter Vossieck and the Development of the Representation Theory of Artin Algebras (2018) (0)

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