Irving Reiner (February 8, 1924 in

Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...

, New York – October 28, 1986 in

Urbana __NOTOC__ Urbana can refer to: Places Italy *Urbana, Italy United States *Urbana, Illinois **Urbana (conference), a Christian conference formerly held in Urbana, Illinois *Urbana, Indiana * Urbana, Iowa *Urbana, Kansas * Urbana, Maryland *Urbana, ...

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. Its largest metropolitan areas include the Chicago metropolitan area, and the Metro East section, of Greater St. Louis. Other smaller metropolita ...

) was a mathematician at the

University of Illinois The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univer ...

who worked on

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

. He solved the problem of finding which

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...

s have a finite number of

indecomposable module In abstract algebra, a module is indecomposable if it is non-zero and cannot be written as a direct sum of two non-zero submodules. Jacobson (2009), p. 111. Indecomposable is a weaker notion than simple module (which is also sometimes called irr ...

s. His book with Charles W. Curtis, , was for many years the standard text on representation theory.

Life

Reiner obtained his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

from

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

in 1947; his dissertation, ''A generalization of Meyer's theorem'', was written under the supervision of Burton Wadsworth Jones. He met another one of Jones' students, Irma Moses, leading to their marriage in August 1948 and two children, Peter Reiner and David Reiner. Reiner met

Hua Luogeng Hua Luogeng or Hua Loo-Keng (; 12 November 1910 – 12 June 1985) was a Chinese mathematician and politician famous for his important contributions to number theory and for his role as the leader of mathematics research and education in the Peop ...

while at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

and subsequently collaborated on three joint papers: * ''On the generators of the symplectic modular group'' (1949); * ''Automorphisms of the unimodular group'' (1951); * ''Automorphisms of the projective unimodular group'' (1952) They remained friends as they attended the

, before Hua returned to his native China and Reiner remained in Illinois.

Bibliography

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References

External links

* *
Irving Reiner memorial award
{{DEFAULTSORT:Reiner, Irving 20th-century American mathematicians University of Illinois Urbana-Champaign faculty People from Brooklyn 1924 births 1986 deaths Mathematicians from New York (state) Cornell University alumni