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.
- Curtis, Charles W.; Reiner, Irving (1962), Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, ISBN 978-0-8218-4066-5, MR 0144979
- Janusz, Gerald J. (1988), "Irving Reiner 1924--1986", Illinois Journal of Mathematics, 32 (3): 315–328, ISSN 0019-2082, MR 947031