Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 5, pp 1323–1338 | Cite as

The \(\pi \)-Semisimplicity of Locally Inverse Semigroup Algebras

  • Yingdan JiEmail author
Original Paper


In this paper, we first characterize when a semigroup has completely 0-simple semigroup as its principal factors. Let R be a commutative ring with an identity, and let S be a locally inverse semigroup with the set of idempotents locally pseudofinite. Assume that the principal factors of S are all completely 0-simple. Then, we prove that the contracted semigroup algebra \(R_0[S]\) is \(\pi \)-semisimple if and only if the contracted semigroup algebras of all the principal factors of S are \(\pi \)-semisimple. Examples are provided to illustrate that the locally pseudofinite condition on the idempotent set of S cannot be removed. Notice that we extend the corresponding results on finite locally inverse semigroups.


Locally inverse semigroup algebras Locally pseudofinite \(\pi \)-Semisimple Completely 0-simple semigroups Principal factors 

Mathematics Subject Classification

16G30 17C17 17C20 17C27 20M25 



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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.School of Applied MathematicsGuangdong University of TechnologyGuangzhouPeople’s Republic of China

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