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

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

14 Scopus citations

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
DOIs	https://doi.org/10.1016/j.jalgebra.2011.02.048
State	Published - 15 Jun 2011
Externally published	Yes

Keywords

Primary
Representations
Secondary
Semigroups
Semirings

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10.1016/j.jalgebra.2011.02.048

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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.",

keywords = "Primary, Representations, Secondary, Semigroups, Semirings",

author = "Zur Izhakian and John Rhodes and Benjamin Steinberg",

note = "Funding Information: E-mail addresses: [email protected] (Z. Izhakian), [email protected], [email protected] (J. Rhodes), [email protected] (B. Steinberg). 1 Supported in part by the ISF (Ref. No. 448/09). 2 Supported in part by NSERC.",

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AU - Rhodes, John

AU - Steinberg, Benjamin

N1 - Funding Information: E-mail addresses: [email protected] (Z. Izhakian), [email protected], [email protected] (J. Rhodes), [email protected] (B. Steinberg). 1 Supported in part by the ISF (Ref. No. 448/09). 2 Supported in part by NSERC.

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 - Primary

KW - Representations

KW - Secondary

KW - Semigroups

KW - Semirings

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SP - 139

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JO - Journal of Algebra

JF - Journal of Algebra

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ER -

Representation theory of finite semigroups over semirings

Abstract

Keywords

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