Cancellative semigroup

About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.

On the Cancellativity of AG-Groupoids

Abstract: An AG-groupoid is a non-associative groupoid in general in which the identity (ab)c = (cb)a holds. In this paper we study some struc- tural properties of AG-groupoids with respect to the cancellativity. We prove that cancellative and non-cancellative elements of an AG-groupoid S parti- tion S and the two classes are AG-subgroupoids of S if S has left identity e. Cancellativity and invertibility coincide in a nite AG-groupoid S with left identity e: For a nite AG-groupoid S with left identity e having at least one non-cancellative element, the set of non-cancellative elements form a maximal ideal. We also prove that for an AG-groupoid S; the conditions (i) S is left cancellative (ii) S is right cancellative (iii) S is cancellative, are equivalent.

On Buchsbaum simplicial affine semigroups

Abstract: We give an arithmetic characterization which allow us to determine algorithmically when the semigroup ring associated to a simplicial affine semigroup is Buchsbaum. This characterization is based on a test performed on the Apery sets of the extremal rays of the semigroup. We use this method to obtain the cardinality of minimal presentations for semigroups with minimal Apery set.

Necessary and sufficient conditions for conservativeness of dynamical semigroups

Abstract: Dynamical semigroups constitute a quantum-mechanical generalization of Markov semigroups, a concept familiar from the theory of stochastic processes. Let ℋ be a Hilbert space andA a von Neumann algebra. A dynamical semigroup Pt is a σ-weakly continuous one-parameter semigroup of completely positive maps ofA into itself. A semigroup Pt possessing the property of preserving the identityI∈A is said to be conservative and its infinitesimal operator L[·] is said to be regular. The present paper studies necessary and sufficient conditions for strongly continuous dynamical semigroups to be conservative. It is shown that under certain additional assumptions one can formulate necessary and sufficient conditions which are analogous to Feller's condition for regularity of a diffusion process: the equation P=L[P] has no solutions inA+. Using a Jensen-type inequality for completely positive maps, constructive sufficient conditions are obtained for conservativeness, in the form of inequalities for commutators. The restriction of a dynamical subgroup to an Abelian subalgebra ofℒ∞(Rn) yields a series of new regularity conditions for both diffusion and jump processes.

Embedding Into Almost Left Factorizable Restriction Semigroups

Abstract: The notion of almost left factorizability and the results on almost left factorizable weakly ample semigroups, due to Gomes and the author, are adapted for restriction semigroups. The main result of the paper is that each restriction semigroup is embeddable into an almost left factorizable restriction semigroup. This generalizes a fundamental result of the structure theory of inverse semigroups.

On fuzzy points in semigroups

Abstract: We consider the semigroup S of the fuzzy points of a semigroup S, and discuss the relation between the fuzzy interior ideals and the subsets of S in an (intra-regular) semigroup S