Representation theory of finite semigroups over semirings

Zur Izhakian, John Rhodes, Benjamin Steinberg

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)139-157
Number of pages19
JournalJournal of Algebra
Volume336
Issue number1
Early online date20 Apr 2011
DOIs
Publication statusPublished - 15 Jun 2011

Fingerprint

Semiring
Representation Theory
Semigroup
Character Theory
Arbitrary
Unit

Keywords

  • representations
  • semirings
  • semigroups

Cite this

Representation theory of finite semigroups over semirings. / Izhakian, Zur; Rhodes, John; Steinberg, Benjamin.

In: Journal of Algebra, Vol. 336, No. 1, 15.06.2011, p. 139-157.

Research output: Contribution to journalArticle

Izhakian, Zur ; Rhodes, John ; Steinberg, Benjamin. / Representation theory of finite semigroups over semirings. In: Journal of Algebra. 2011 ; Vol. 336, No. 1. pp. 139-157.
@article{1e9297ea3db7474fba8d74c5425a868b,
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.",
keywords = "representations, semirings, semigroups",
author = "Zur Izhakian and John Rhodes and Benjamin Steinberg",
year = "2011",
month = "6",
day = "15",
doi = "10.1016/j.jalgebra.2011.02.048",
language = "English",
volume = "336",
pages = "139--157",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Representation theory of finite semigroups over semirings

AU - Izhakian, Zur

AU - Rhodes, John

AU - Steinberg, Benjamin

PY - 2011/6/15

Y1 - 2011/6/15

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

VL - 336

SP - 139

EP - 157

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -