ℛ-unipotent semigroup algebras
Yingdan Ji · Communications in Algebra · 2017
Let S be an ℛ-unipotent semigroup such that the idempotent set E(S) is locally ℒ-finite, and let R be a commutative ring with identity. In this paper, we construct a set of orthogonal idempotents {eỸ|Y∈(S∕ℒ)∗} in R0[S], then prove that ℬ¯={eLa†̃aeLa∗̃|a∈S∗} is an R-basis of R0[S], and that the set S¯=ℬ¯∪{0} is a 0-direct union of ℛ-unipotent completely 0-simple semigroups. As an application, we show that R0[S] is π-semisimple if and only if S is an inverse semigroup and for each maximal subgroup G of S, the group algebra R[G] is π-semisimple.