Rings Associated to Bands with Two Components

Ferran Cedó; Elena Rodríguez-Jorge

doi:10.1080/00927870903337950

Rings Associated to Bands with Two Components

Ferran Cedó, Elena Rodríguez-Jorge

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

Abstract

A band is a semigroup whose elements are idempotents. It is proved that for any field K the commutative K-algebra, constructed in [2], associated to a band S with two components E, F such that EFE = F, is a reduced ring. Thus the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative reduced K-algebra. © 2010 Copyright Taylor and Francis Group, LLC.

Original language	English
Pages (from-to)	4117-4129
Journal	Communications in Algebra
Volume	38
Issue number	11
DOIs	https://doi.org/10.1080/00927870903337950
Publication status	Published - 1 Nov 2010

Keywords

Band
Reduced ring
Semigroup algebra
Triangular matrices

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10.1080/00927870903337950

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abstract = "A band is a semigroup whose elements are idempotents. It is proved that for any field K the commutative K-algebra, constructed in [2], associated to a band S with two components E, F such that EFE = F, is a reduced ring. Thus the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative reduced K-algebra. {\textcopyright} 2010 Copyright Taylor and Francis Group, LLC.",

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AU - Rodríguez-Jorge, Elena

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AB - A band is a semigroup whose elements are idempotents. It is proved that for any field K the commutative K-algebra, constructed in [2], associated to a band S with two components E, F such that EFE = F, is a reduced ring. Thus the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative reduced K-algebra. © 2010 Copyright Taylor and Francis Group, LLC.

KW - Band

KW - Reduced ring

KW - Semigroup algebra

KW - Triangular matrices

U2 - 10.1080/00927870903337950

DO - 10.1080/00927870903337950

M3 - Article

SN - 0092-7872

VL - 38

SP - 4117

EP - 4129

JO - Communications in Algebra

JF - Communications in Algebra

IS - 11

ER -

Rings Associated to Bands with Two Components

Abstract

Keywords

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