Irving Reiner
Encyclopedia
Irving Reiner was a mathematician at the University of Illinois who worked on representation theory
. He solved the problem of finding which abelian group
s have a finite number of indecomposable module
s. His book with Charles W. Curtis
, , was for many years the standard text on representation theory.
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 studiesmodules over these abstract algebraic structures...
. He solved the problem of finding which abelian group
Abelian group
In abstract algebra, 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 their order . Abelian groups generalize the arithmetic of addition of integers...
s have a finite number of indecomposable module
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:simple means "no proper submodule" N...
s. His book with Charles W. Curtis
Charles W. Curtis
Charles W. Curtis is a mathematician and historian of mathematics, known for his work in finite group theory and representation theory. He is a retired professor of mathematics at the University of Oregon.-Research:...
, , was for many years the standard text on representation theory.