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 M R GJ , mJ , nJ ;PJ with J ∈ S/J, where mJ is the number of R-classes in J , nJ the number of L-classes in J , and GJ a maximum subgroup of J . As applications, we obtain the sufficient and necessary conditions for the semigroup ...

Let A be an algebra over a field K, m and n natural numbers P = (pji) fixed x matrix A. The K-vector space of all matrices the can made into with respect to following operation (o): B o C BPC. This is called Munn sandwich P. algebras such type arose as generalizations semigroup Rees semigroups which in turn are closely related simple semigroups. article describes generators defining relations M...

By a 'representation' we shall mean throughout a representation by n x n matrices with entries from an arbitrary (commutative) field. Clifford has constructed all representations of completely simple semigroups [1; 4]. Munn has determined the representations of finite semigroups for which the corresponding semigroup algebra is semi-simple [6]. It is noted by Clifford and Preston [4] that if S i...

We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...

Work of Clifford, Munn and Ponizovskĭı parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich. All of these approaches make use of Rees’s theorem characterizing 0-simple...

In this paper, we prove that the algebra of an étale groupoid with totally disconnected unit space has a simple over field if and only is minimal effective function vanishes on every open subset null function. Previous work subject required to be also topologically principal in non-Hausdorff case, but do not. Furthermore, provide first examples not groupoids spaces. Our come from self-similar g...