Irving Reiner (February 8, 1924 in Brooklyn, New York – October 28, 1986) 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, (Curtis & Reiner 1962), was for many years the standard text on representation theory.
Reiner obtained his Ph.D.
from Cornell University in 1947; his dissertation, A generalization of Meyer's theorem, was written under the supervision of Burton Wadsworth Jones.