Representation Theory of Finite Semigroups over Semirings
Rings and Algebras
2010-04-13 v1 Representation Theory
Abstract
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the results for a field. Special attention is paid to the boolean semiring, where we also characterize the simple representations and introduce the beginnings of a character theory.
Keywords
Cite
@article{arxiv.1004.1660,
title = {Representation Theory of Finite Semigroups over Semirings},
author = {Zur Izhakian and John Rhodes and Benjamin Steinberg},
journal= {arXiv preprint arXiv:1004.1660},
year = {2010}
}