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, a semigroup is locally testable if it is k-testable for some k > 0, where k is the number of subwords of length k of the words a and b. The structure of local testable semigroups is studied and sufficient conditions for local testability are given.
Abstract: Let S be a semigroup of words over an alphabet ∑ . Suppose tliar every two words u and e over ∑ are equal in S if (1) the sets of subwords of length k of the words a and b coincide and are non-empty. (2) the prefix (suffix) of u of length k1 is equal to the prefix (suffix) of e. Then S is called k-testable. A semigroup is locally testable if it is k-testable for some k > 0. We present a finite basis of identities of the variety of A'-testable semigroups. The structure of k-testable semigroup is studied. Necessarv and sufficient conditions for local testability will be given. A solution to one problem from the survey of Shevrin and Sukhanov (1985) will be presented.
17 citations
TL;DR: It is shown that every regular unambiguous semigroup is isomorphic to an iterative Morita semigroup of a special form by relying on Morita theory.
Abstract: In recent work we associated a natural category to a semigroup and developed Morita theory for semigroups. In particular we gave a generalisation of Rees’ Theorem which led us to define what we call a Morita semigroup, this is our analogue of a structure matrix semigroup. In this article we formulate a method for extending Morita semigroups by groups. We say that a semigroup is an iterative Morita semigroup if it is obtained by successive applications of pasting families of Morita semigroups which have been extended by groups. By relying on Morita theory we show that every regular unambiguous semigroup is isomorphic to an iterative Morita semigroup of a special form. Our result can be viewed as a co-ordinate free version of the Synthesis Theorem.
17 citations
TL;DR: In this article, it was shown that the automorphisms of the endomorphism semigroup of a free inverse semigroup are inner and determine all isomorphisms between them.
Abstract: We prove that automorphisms of the endomorphism semigroup of a free inverse semigroup are inner and determine all isomorphisms between the endomorphism semigroups of free inverse semigroups.
17 citations
01 Feb 1973
TL;DR: Theorem 3 relates this class of semigroups to left amenable semigroup as mentioned in this paper and further the class of all semiigroups with this property, where the convolution powers p(n) of P implied by the above property are studied.
Abstract: Let S be a discrete semigroup, P a probability measure on S and SF S with limsupn(P0,)(s))1/n=1. We study limit theorems for the convolution powers p(n) of P implied by the above property and further the class of all semigroups with this property. Theorem 3 relates this class of semigroups to left amenable semigroups.
17 citations
TL;DR: In this article, a series of Lipschitz dual notions were developed to establish an analysis approach to Lipschnitzian semigroup, and it was proved that a (nonlinear) nonlinear Lipschi-semigroup can be isometrically embedded into a certain C 0 -semigroup.
Abstract: Lipschitzian semigroup refers to a one-parameter semigroup of Lipschitz operators that is strongly continuous in the parameter. It contains C 0 -semigroup, nonlinear semigroup of contractions and uniformly k-Lipschitzian semigroup as special cases. In this paper, through developing a series of Lipschitz dual notions, we establish an analysis approach to Lipschitzian semigroup. It is mainly proved that a (nonlinear) Lipschitzian semigroup can be isometrically embedded into a certain C 0 -semigroup. As application results, two representation formulas of Lipschitzian semigroup are established, and many asymptotic properties of C 0 -semigroup are generalized to Lipschitzian semigroup.
17 citations