International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 576061, 5 pages
Research Article

A Note on Locally Inverse Semigroup Algebras

Xiaojiang Guo

Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Received 9 December 2007; Accepted 29 January 2008

Academic Editor: Francois Goichot

Copyright © 2008 Xiaojiang Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 direct product of Munn algebras (R[GJ],mJ,nJ;PJ) with JS/𝒥, where mJ is the number of -classes in J, nJ the number of -classes in J, and GJ a maximum subgroup of J. As applications, we obtain the sufficient and necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple.