Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: In this paper, order-preserving semigroup actions on posets are finitely axiomatized in terms of order preserving semigroups of partial functions equipped with the first projection quasi-order.
Abstract: Structures consisting of a semigroup of (partial) functions on a set X, a poset of subsets of X, and a preimage operation linking the two, arise commonly throughout mathematics. The poset may be equipped with one or more set operations, up to Boolean algebra structure. Such structures are finitely axiomatized here in terms of order-preserving semigroup actions on posets. This generalises Schein’s axiomatization of semigroups of partial functions equipped with the first projection quasi-order.
3 citations
01 Jan 1990
TL;DR: A survey of results on the Jacobson radical of the semigroup ring of a completely regular semigroup over a ring with unity is given in this article, where a semigroup S is said to be completely regular if and only if it is covered by its subgroups.
Abstract: A semigroup S is said to be completely regular if and only if it is covered by its subgroups; that is, if and only if, for each a ∈ S, a ∈ a2 S∩S a2. Groups and bands (semigroups of idempotents) are extreme special cases. In this paper a survey is given of results on the Jacobson radical of the semigroup ring of a completely regular semigroup over a ring with unity. Much of the inspiration is derived from the study of group rings, in which a similar interplay of two distinct branches of algebra is apparent. The work discussed covers a period of some thirty- six years, from the first paper on semigroup rings by Marianne Teissier (1952) to the present day.
3 citations
3 citations
19 Jun 1989
TL;DR: In this article, the authors give an example of a positive semigroup on a Banach lattice whose semigroup dual is not a BLS. And they show that a positive semi-group on a BSL can be represented by a positive non-convex semigroup.
Abstract: We give an example of a positive semigroup on a Banach lattice whose semigroup dual is not a Banach lattice.
3 citations
01 Jan 1996
TL;DR: In this paper, it was shown that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup, and that the semigroup algebra of every linear cancellation semigroup is semisimple.
Abstract: We consider algebras over a field of characteristic zero, and prove that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup. It follows that the semigroup algebra of every linear cancellative semigroup is semisimple. © 1996 American Mathematical Society.
3 citations