Journal ArticleDOI
Semiprimitivity of inverse semigroup algebras
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This article is published in Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences.The article was published on 1982-01-01. It has received 17 citations till now. The article focuses on the topics: Cancellative semigroup & Bicyclic semigroup.read more
Citations
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Simplicity, primitivity and semiprimitivity of étale groupoid algebras with applications to inverse semigroup algebras
TL;DR: In this paper, simplicity, primitivity and semiprimitivity of algebras associated to etale groupoids are studied and the results are used to recover the known primitivity criterion for Leavitt path algesbras.
Journal ArticleDOI
On commutative semigroup algebras
TL;DR: In this article, the problem of finding necessary and sufficient conditions on a commutative semigroup S for the algebra FS of S over a field F to be semiprimitive (Jacobson semisimple) was studied.
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Prime étale groupoid algebras with applications to inverse semigroup and Leavitt path algebras
TL;DR: In this paper, the authors give sufficient and necessary conditions for an etale groupoid algebra to be a prime ring and obtain analogous results for semiprimeness for inverse semigroup algebras.
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
Book
The Algebraic Structure of Group Rings
TL;DR: For a group G over an integral domain R the group ring R(G) is a free unitary i-module over the elements of G as a basis and in which the multiplication on G is extended linearly to yield an associative multiplication on R (G), becoming a ring with an identity.
Journal ArticleDOI
On semigroup algebras
TL;DR: In the classical theory of representations of a finite group by matrices over a field, the concept of the group algebra (group ring) over is of fundamental importance as discussed by the authors, and the main property of such an algebra is that it is semi-simple, provided that the characteristic of is zero or a prime not dividing the order of the groups.
Journal ArticleDOI
Free Inverse Semigroups
TL;DR: In this article, a graph-theoretic technique for representing the elements of the free inverse semigroup FIA is presented, based on the notion of a word-tree on a set A. With the aid of this technique various properties of FIA are easily deduced.