Irving Rainer (February 8, 1924 in

Brooklyn Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelv ...

New York New York most commonly refers to: * New York (state), a state in the northeastern United States * New York City, the most populous city in the United States, located in the state of New York New York may also refer to: Places United Kingdom * ...

– October 28, 1986 in Urbana,

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. It borders on Lake Michigan to its northeast, the Mississippi River to its west, and the Wabash River, Wabash and Ohio River, Ohio rivers to its ...

) was a mathematician at the

University of Illinois The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public university, public land-grant university, land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United ...

who worked on

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

. 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 commu ...

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. Indecomposable is a weaker notion than simple module (which is also sometimes called irreducible module): simple ...

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

Life

Reiner obtained his Ph.D. from

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

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) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

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

* * *

References

External links

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