TY - JOUR

T1 - On the semigroup algebra of binary relations

AU - Bremner, Murray R.

AU - El Bachraoui, Mohamed

N1 - 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 .

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 - http://www.scopus.com/inward/record.url?scp=77957727128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957727128&partnerID=8YFLogxK

U2 - 10.1080/00927870902939418

DO - 10.1080/00927870902939418

M3 - Article

AN - SCOPUS:77957727128

VL - 38

SP - 3499

EP - 3505

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 9

ER -