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

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	4117-4129
Revista	Communications in Algebra
Volum	38
Número	11
DOIs	https://doi.org/10.1080/00927870903337950
Estat de la publicació	Publicada - 1 de nov. 2010

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10.1080/00927870903337950

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title = "Rings Associated to Bands with Two Components",

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.",

keywords = "Band, Reduced ring, Semigroup algebra, Triangular matrices",

author = "Ferran Ced{\'o} and Elena Rodr{\'i}guez-Jorge",

year = "2010",

month = nov,

day = "1",

doi = "10.1080/00927870903337950",

language = "English",

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pages = "4117--4129",

journal = "Communications in Algebra",

issn = "0092-7872",

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T1 - Rings Associated to Bands with Two Components

AU - Cedó, Ferran

AU - Rodríguez-Jorge, Elena

PY - 2010/11/1

Y1 - 2010/11/1

N2 - 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.

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

Resum

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