Book ChapterDOI
A Class of Inverse Semigroup Algebras
W. D. Munn
- pp 111-119
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In this article, it was shown that if the semi-lattice of an inverse semigroup S satisfies a certain finiteness condition, introduced by Teply, Turman and Quesada in 1980, then the converse does hold.Abstract:
In 1976, Domanov showed that the algebra of an inverse semigroup S over a field F is semiprimitive (that is, has zero Jacobson radical) if the algebra of each maximal subgroup of S over F is semiprimitive. It is known that the converse statement is false in general. The principal purpose of this paper is to announce that if the semi-lattice of S satisfies a certain finiteness condition, introduced by Teply, Turman and Quesada in 1980, then the converse does hold. Corresponding results for primitivity are also discussed.read more
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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.