Representation theory of finite semigroups over semirings

Zur Izhakian; John Rhodes; Benjamin Steinberg

doi:10.1016/j.jalgebra.2011.02.048

Representation theory of finite semigroups over semirings

Zur Izhakian
, John Rhodes
, Benjamin Steinberg

Mathematical Science

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	139-157
Number of pages	19
Journal	Journal of Algebra
Volume	336
Issue number	1
Early online date	20 Apr 2011
DOIs	https://doi.org/10.1016/j.jalgebra.2011.02.048
Publication status	Published - 15 Jun 2011

Keywords

representations
semirings
semigroups

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title = "Representation theory of finite semigroups over semirings",

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.",

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AU - Rhodes, John

AU - Steinberg, Benjamin

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N2 - 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.

AB - 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.

KW - representations

KW - semirings

KW - semigroups

U2 - 10.1016/j.jalgebra.2011.02.048

DO - 10.1016/j.jalgebra.2011.02.048

M3 - Article

SN - 0021-8693

VL - 336

SP - 139

EP - 157

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Representation theory of finite semigroups over semirings

Abstract

Keywords

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