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
SN - 0092-7872
VL - 38
SP - 3499
EP - 3505
JO - Communications in Algebra
JF - Communications in Algebra
IS - 9
ER -