Maurice Auslander
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American mathematician and professor
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Maurice Auslandermathematics Degrees
Mathematics
#2135
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#3341
Historical Rank
#854
USA Rank
Measure Theory
#861
World Rank
#1133
Historical Rank
#322
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Mathematics
Maurice Auslander's Degrees
- PhD Mathematics University of Chicago
Why Is Maurice Auslander Influential?
(Suggest an Edit or Addition)According to Wikipedia, Maurice Auslander was an American mathematician who worked on commutative algebra, homological algebra and the representation theory of Artin algebras . He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras.
Maurice Auslander's Published Works
Published Works
- Representation Theory of Artin Algebras I (1974) (1769)
- Stable Module Theory (1969) (1074)
- Representation Theory of Artin Algebras: Contents (1995) (1021)
- The Brauer group of a commutative ring (1960) (697)
- Applications of contravariantly finite subcategories (1991) (679)
- Preprojective modules over artin algebras (1980) (503)
- Representation Theory of Artin Algebras II (1974) (462)
- Representation theory of artin algebras iii almost split sequences (1975) (407)
- The Homological Theory of Maximal Cohen-Macaulay Approximations (1989) (398)
- Almost split sequences in subcategories (1981) (392)
- Coxeter functors without diagrams (1979) (278)
- Codimension and Multiplicity (1958) (235)
- Representation theory of artin algebras IV1)Invariants given by almost split sequences (1977) (204)
- Rational singularities and almost split sequences (1986) (198)
- Modules over unramified regular local rings (1961) (196)
- On the Dimension of Modules and Algebras (III): Global Dimension (1955) (190)
- Homological dimension in local rings (1957) (184)
- Stable equivalence of dualizing R-varieties* (1974) (179)
- On a generalized version of the Nakayama conjecture (1975) (178)
- Isolated singularities and existence of almost split sequences (1986) (166)
- Liftings and Weak Liftings of Modules (1993) (133)
- Cohen-Macaulay and Gorenstein Artin algebras (1991) (131)
- Large Modules over Artin Algebras (1976) (112)
- Stable equivalence of artin algebras (1973) (111)
- Homological theory of idempotent ideals (1992) (108)
- On Ramification Theory in Noetherian Rings (1959) (106)
- Representation theory of artin algebras v: methods for computing aimost split sequences and irreducible morphisms (1977) (98)
- Modules determined by their composition factors (1985) (88)
- k-Gorenstein algebras and syzygy modules (1994) (84)
- Relative homology and representation theory 1 (1993) (84)
- Syzygy Modules for Noetherian Rings (1996) (82)
- HOMOLOGICAL DIMENSION IN NOETHERIAN RINGS. (1956) (82)
- On the purity of branch locus (1962) (82)
- Representation theory of artin algebras VI: A functorial approach to aimost split sequences (1978) (78)
- Relative homology and representation theory I. Relative homology and homologically finite subcategories (75)
- UNIQUE FACTORIZATION IN REGULAR LOCAL RINGS. (1959) (65)
- Relative homology and representation theory II: Relative Cotilting theory (1993) (57)
- A functorial approach to representation theory (1982) (57)
- Commutator Subgroups of Free Groups (1955) (54)
- On regular group rings (1957) (52)
- Almost-split sequences and group rings (1986) (51)
- Brauer groups of discrete valuation rings (1968) (48)
- Grothendieck groups of algebras and orders (1986) (45)
- Almost split sequences I (1975) (41)
- McKay quivers and extended Dynkin diagrams (1986) (41)
- Relative homology and representation theory III: Cotilting modules and Wedderburn correspondence (1993) (41)
- The Cohen-Macaulay type of Cohen-Macaulay rings (1989) (40)
- Homological dimension in noetherian rings. II (1958) (38)
- Almost split sequences for rational double points (1987) (35)
- Selected works of Maurice Auslander (1999) (34)
- Gorenstein algebras and algebras with dominant dimension at least 2 (1993) (34)
- A characterization of orders of finite lattice type (1972) (33)
- Relations for Grothendieck groups of Artin algebras (1984) (31)
- Almost split sequences for Cohen-Macaulay-modules (1987) (30)
- On the Representation Type of Triangular Matrix Rings (1976) (28)
- Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and their Completions (1989) (28)
- Representations of Algebras and Related Topics: Homologically finite subcategories (1992) (27)
- Ramification index and multiplicity (1963) (26)
- Comments on the functor ext (1969) (26)
- Almost split sequences for ℤ-graded rings (1987) (26)
- Representations of Algebras: A survey of existence theorems for almost split sequences (1986) (23)
- Addendum to “almost split sequences in subcategories”☆ (1981) (23)
- Galois actions on rings and finite Galois coverings. (1989) (22)
- Groups, rings, modules (1974) (20)
- Almost split sequences in dimension two (1987) (19)
- Almost Split Sequences whose Middle Term has at most Two Indecomposable Summands (1979) (19)
- Modules with waists (1975) (18)
- Stable equivalence of dualizing R-varieties. V. Artin algebras stably equivalent to hereditary algebras (1975) (17)
- Relative homology and representation theory III (16)
- Adjoint Functors and an Extension of the Green Correspondence for Group Representations (1994) (15)
- Stable equivalence of dualizing -varieties. II. Hereditary dualizing -varieties (1975) (14)
- On the Dimension of Modules and Algebras, VI. Comparison of Global and Algebra Dimension (1957) (14)
- Remarks on a Theorem of Bourbaki (1966) (14)
- Stable equivalence of dualizing R-varieties. III. Dualizing R-varieties stably equivalent to hereditary dualizing R-varieties☆ (1975) (13)
- Solvable Lie groups and locally euclidean Riemann spaces (1958) (12)
- INVARIANT FACTORS AND TWO CRITERIA FOR PROJECTIVITY OF MODULES (1962) (12)
- Representations of Algebras: Almost split sequences and algebraic geometry (1986) (11)
- Lattices over orders: finitely presented functors and preprojective partitions (1982) (10)
- Corrections to Codimension and Multiplicity (1959) (9)
- Preprojective modules: An introduction and some applications (1980) (8)
- Dimension of Ideals in Polynomial Rings (1958) (8)
- Finite type implies isolated singularity (1985) (7)
- Grothendieck groups of algebras with nilpotent annihilators (1988) (6)
- Preprojective lattices over classical orders (1981) (6)
- Stable equivalence of dualizing R-varieties. IV. Higher global dimension (1975) (5)
- RELATIVE HOMOLOGY (5)
- Periodic modules over weakly symmetric algebras (1977) (5)
- Almost split sequences for abelian group graded rings (1988) (4)
- Trace quotient modules (1988) (4)
- Graded modules and their completions (1990) (3)
- Remark on automorphisms of groups (1958) (3)
- Modules over endomorphism rings (1992) (2)
- Representations of Algebras: Workshop Notes of the Third International Conference on Representations of Algebras Held in Puebla, Mexico, August 4-8, 1980 (1982) (1)
- Modules having waists (1975) (1)
- Representation Theory of Artin Algebras: Conjectures (1995) (1)
- Representations of Algebras (1981) (1)
- A Remark on a Paper of M. Hironaka (1962) (1)
- Representation Theory of Artin Algebras: Modules determining morphisms (1995) (1)
- Relevant conference proceedings (1995) (0)
- Finite representation type (1995) (0)
- Representation Theory of Artin Algebras: Notation (1995) (0)
- Review: O. Zariski and P. Samuel, Commutative algebra (1962) (0)
- Representation Theory of Artin Algebras: Examples of algebras and modules (1995) (0)
- Representation Theory of Artin Algebras: The transpose and the dual (1995) (0)
- Representation Theory of Artin Algebras: Open problems (1995) (0)
- Representation Theory of Artin Algebras: The Auslander–Reiten-quiver (1995) (0)
- Representation Theory of Artin Algebras: Stable equivalence (1995) (0)
- Representation Theory of Artin Algebras: Bibliography (1995) (0)
- Representation Theory of Artin Algebras: Hereditary algebras (1995) (0)
- Representation Theory of Artin Algebras: Short chains and cycles (1995) (0)
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