TY - JOUR
A2 - Goichot, Francois
AU - Guo, Xiaojiang
PY - 2008
DA - 2008/03/23
TI - A Note on Locally Inverse Semigroup Algebras
SP - 576061
VL - 2008
AB - Let R be a commutative ring and S a finite locally inverse semigroup.It is proved that the semigroup algebra R[S] is isomorphic to the directproduct of Munn algebras ℳ(R[GJ],mJ,nJ;PJ) with J∈S/𝒥, wheremJ is the number of ℛ-classes in J, nJ the number of ℒ-classes in J, andGJ a maximum subgroup of J. As applications, we obtain the sufficientand necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple.
SN - 0161-1712
UR - https://doi.org/10.1155/2008/576061
DO - 10.1155/2008/576061
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi Publishing Corporation
KW -
ER -