Irving Reiner
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Mathematician
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Mathematics
Irving Reiner's Degrees
- PhD Mathematics University of Chicago
Why Is Irving Reiner Influential?
(Suggest an Edit or Addition)According to Wikipedia, Irving Reiner was a mathematician at the University of Illinois who worked on representation theory. He solved the problem of finding which abelian groups have a finite number of indecomposable modules. His book with Charles W. Curtis, , was for many years the standard text on representation theory.
Irving Reiner'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
- Representation theory of finite groups and associated algebras (1962) (3126)
- Methods of Representation Theory (1981) (1613)
- Methods of representation theory--with applications to finite groups and orders (1981) (716)
- ASSOCIATIVE ALGEBRAS(Graduate Texts in Mathematics, 88) (1983) (172)
- Representations of Cyclic Groups in Rings of Integers, II (1962) (97)
- Integral representations of cyclic groups of prime order (1957) (95)
- Integral representations and diagrams. (1978) (79)
- Automorphisms of the unimodular group (1951) (74)
- On the generators of the symplectic modular group (1949) (63)
- A Mayer-Vietoris sequence for class groups (1974) (60)
- Zeta functions of arithmetic orders and Solomon's conjectures (1980) (54)
- On the number of matrices with given characteristic polynomial (1961) (46)
- A survey of integral representation theory (1970) (42)
- Class groups for integral representations of metacyclic groups (1972) (39)
- Class Groups and Picard Groups of Group Rings and Orders (1976) (32)
- Normal subgroups of the unimodular group (1958) (27)
- Class groups of integral group rings (1972) (26)
- A New Type of Automorphism of the General Linear Group Over a Ring (1957) (24)
- Grothendieck groups of orders in semisimple algebras (1964) (22)
- Class Groups and Picard Groups of Orders (1974) (22)
- Orders and their Applications (1985) (21)
- Automorphisms of the symplectic modular group (1955) (19)
- AUTOMORPHISMS OF THE GENERAL LINEAR GROUP OVER A PRINCIPAL IDEAL DOMAIN (1957) (19)
- Relative Grothendieck groups (1969) (19)
- The integral representation ring of a finite group. (1965) (18)
- Zeta functions of integral representations (1980) (17)
- Equivalence of representations under extensions of local ground rings (1961) (17)
- Grothendieck groups of integral group rings (1965) (16)
- Real linear characters of the symplectic modular group (1955) (16)
- Failure of the Krull-Schmidt theorem for integral representations. (1962) (16)
- The Krull-Schmidt theorem for integral group representations (1961) (15)
- The Schur index in the theory of group representations. (1961) (14)
- Nilpotent elements in rings of integral representations (1966) (14)
- Projective class groups of symmetric and alternating groups (1975) (12)
- Relations between integral and modular representations. (1966) (12)
- Matrix Completions Over Dedekind Rings (1981) (11)
- INTEGRAL REPRESENTATION ALGEBRAS( (1966) (11)
- Integral representations of finite groups (1978) (11)
- On groups with finitely many indecomposable integral representations (1962) (10)
- Congruence subgroups of matrix groups. (1956) (10)
- Relative Grothendieck rings (1969) (10)
- Solomon's conjectures and the local functional equation for zeta functions of orders (1980) (10)
- Reduction theorems for relative Grothendieck rings (1969) (10)
- Integral representations of cyclic groups of order (1976) (10)
- Automorphisms of the two-dimensional general linear group over a Euclidean ring (1958) (10)
- L-functions of arithmetic orders and asymptotic distribution of ideals. (1981) (9)
- Modular representation algebras (1967) (9)
- On the Class Number of Representations of an Order (1959) (9)
- Topics in integral representation theory (1979) (9)
- Restriction maps on relative grothendieck rings (1970) (9)
- Subgroups of the unimodular group (1961) (9)
- Invariants of integral representations. (1978) (8)
- A survey of analytic methods in noncommutative number theory (1985) (8)
- Automorphisms of the Gaussian unimodular group (1958) (8)
- Integral represetation algebras (1966) (8)
- The Number of Cross-Join Pairs in Maximum Length Linear Sequences (1991) (8)
- Symplectic modular complements (1954) (8)
- Representation Theory of Finite Groups and Related Topics (1971) (7)
- Automorphisms of the projective unimodular group (1952) (7)
- Indecomposable representations of non-cyclic groups. (1962) (7)
- The prime ideal theorem in non-commutative arithmetic (1982) (7)
- Maschke Modules Over Dedekind Rings (1956) (7)
- On the number of irreducible modular representations of a finite group (1964) (6)
- Introduction to matrix theory and linear algebra (1971) (6)
- Finite generation of Grothendieck rings relative to cyclic subgroups. (1969) (6)
- A Proof of the Normal Basis Theorem (1975) (6)
- Lifting Isomorphisms of Modules (1979) (5)
- Module extensions and blocks (1967) (5)
- Maximal sets of involutions (1955) (5)
- Functional equations for L-functions of arithmetic orders. (1981) (4)
- INTEGRAL REPRESENTATIONS OF CYCLIC p-GROUPS (1978) (4)
- AMERICAN MATHEMATICAL SOCIETY. (4)
- An excision theorem for Grothendieck rings (1970) (4)
- Zeta-functions of orders (1981) (3)
- Analytic continuation of partial zeta functions of arithmetic orders. (1984) (3)
- New asymptotic formulas for the distribution of left ideals of orders. (1986) (3)
- Locally free class groups of orders (1975) (3)
- The nonuniqueness of irreducible constituents of integral group representations (1960) (3)
- Extensions of irreducible modules. (1963) (3)
- Functional equations for Hurwitz series and partial zeta functions of orders. (1986) (3)
- Functions not Formulas for Primes (1943) (3)
- Class groups of orders and a mayer-vietoris sequence (1973) (2)
- A theorem on continued fractions (1957) (2)
- Zeta functions and composition factors for arithmetic orders (1987) (2)
- Behavior of integral group representations under ground ring extension (1960) (2)
- Integral representations: Genus, k-theory and class groups (1978) (2)
- LEFT-VS-RIGHT ZETA-FUNCTIONS (1984) (2)
- Completion of Primitive Matrices (1966) (2)
- On Diederichsen's formula for extensions of lattices (1979) (1)
- Orders and Their Applications: Proceedings of a Conference Held in Oberwolfach, West Germany June 3-9, 1984 (1985) (1)
- A generalization of Meyer’s theorem (1949) (1)
- Erratum to ntegral Representations of Cyclic Groups of Order p 2 (1977) (0)
- Introduction to Matrix Theory and Linear Algebra.@@@Linear Algebra.@@@Elements of Linear Algebra.@@@Linear Algebra with Applications: Including Linear Programming.@@@Linear Algebra and Group Theory.@@@Matrix Methods in Urban and Regional Analysis. (1973) (0)
- The effect of an involution in $$\widetilde{K}^0 $$ (ZG) (1968) (0)
- AN ASYMPTOTIC RESULT FOR SUBGROUPS OF SL(2, Z) OF LEVEL 2 (0)
- Erratum to: “Integral representations of cyclic groups of order ²” (Proc. Amer. Math. Soc. 58 (1976), 8–12) (1977) (0)
- On genera of binary quadratic forms (1945) (0)
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