On the semigroup algebra of binary relations

Murray R. Bremner; Mohamed El Bachraoui

doi:10.1080/00927870902939418

On the semigroup algebra of binary relations

Murray R. Bremner
, Mohamed El Bachraoui

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

4 Citations (Scopus)

Abstract

The semigroup of binary relations on {1,. . .;., n} with the relative product is isomorphic to the semigroup B_n of n × n zero-one matrices with the Boolean matrix product. Over any field F, we prove that the semigroup algebra FB_n contains an ideal K_n of dimension (2ⁿ-1)², and we construct an explicit isomorphism of K_n with the matrix algebra M2n-1(F).

Original language	English
Pages (from-to)	3499-3505
Number of pages	7
Journal	Communications in Algebra
Volume	38
Issue number	9
DOIs	https://doi.org/10.1080/00927870902939418
Publication status	Published - 2010
Externally published	Yes

Keywords

Binary relations
Boolean matrices
Representational theory
Semigroup algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870902939418

Cite this

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title = "On the semigroup algebra of binary relations",

abstract = "The semigroup of binary relations on \{1,. . .;., n\} with the relative product is isomorphic to the semigroup Bn of n × n zero-one matrices with the Boolean matrix product. Over any field F, we prove that the semigroup algebra FBn contains an ideal Kn of dimension (2n-1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n-1(F).",

keywords = "Binary relations, Boolean matrices, Representational theory, Semigroup algebras",

author = "Bremner, \{Murray R.\} and \{El Bachraoui\}, Mohamed",

note = "Funding Information: Murray Bremner thanks NSERC for financial support, the School of Science and Engineering at Al-Akhawayn University in Ifrane (Morocco) for its hospitality during his visit in May 2007, and Shaun Fallat for a helpful remark about the matrix .",

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AU - El Bachraoui, Mohamed

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PY - 2010

Y1 - 2010

N2 - The semigroup of binary relations on {1,. . .;., n} with the relative product is isomorphic to the semigroup Bn of n × n zero-one matrices with the Boolean matrix product. Over any field F, we prove that the semigroup algebra FBn contains an ideal Kn of dimension (2n-1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n-1(F).

AB - The semigroup of binary relations on {1,. . .;., n} with the relative product is isomorphic to the semigroup Bn of n × n zero-one matrices with the Boolean matrix product. Over any field F, we prove that the semigroup algebra FBn contains an ideal Kn of dimension (2n-1)2, and we construct an explicit isomorphism of Kn with the matrix algebra M2n-1(F).

KW - Binary relations

KW - Boolean matrices

KW - Representational theory

KW - Semigroup algebras

UR - https://www.scopus.com/pages/publications/77957727128

UR - https://www.scopus.com/pages/publications/77957727128#tab=citedBy

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 9

ER -

On the semigroup algebra of binary relations

Abstract

Keywords

ASJC Scopus subject areas

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