Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 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
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TL;DR: In this article, a spectral mapping theorem for continuous semigroups of operators on any Banach space is presented, where the condition for the hyperbolicity of a semigroup on the Banach spaces is given in terms of the generator of an evolutionary semigroup acting in the space of functions.
Abstract: We present a spectral mapping theorem for continuous semigroups of operators on any Banach space $E$. The condition for the hyperbolicity of a semigroup on $E$ is given in terms of the generator of an evolutionary semigroup acting in the space of $E$-valued functions. The evolutionary semigroup generated by the propagator of a nonautonomous differential equation in $E$ is also studied. A ``discrete'' technique for the investigating of the evolutionary semigroup is developed and applied to describe the hyperbolicity (exponential dichotomy) of the nonautonomuos equation.
File Length: 68K
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
TL;DR: In this paper, the structure of J-bisimpleimple semigroups mod groups and a determination of several of their properties are presented. But they do not specify a generalization of the bicyclic semigroup and indicate an application of this result.
Abstract: If 5 is a semigroup, Es will denote the collection of idempotents of 5. A bisimple semigroup S is called J-bisimple if and only if Es = {eiiÇzI, the integers} with e^e^ if and only if i^j. We announce the determination of the structure of J-bisimple semigroups mod groups and a determination of several of their properties. We also give a certain generalization of the bicyclic semigroup and indicate an application of this result. We use the notation and terminology of [2],
3 citations