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, it was shown that every weakly continuous contractive semigroup of operators on a dense sub-semigroup of the positive real numbers can be extended to semigroups over the real numbers.
Abstract: Let S be a dense sub-semigroup of the positive real numbers, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over the positive real numbers. We obtain similar results for non-linear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over the positive real numbers.
3 citations
TL;DR: In this article, the notion of a w-class of semigroups was introduced and it was shown that every endomorphism semigroup of a free product of a semigroup from a maximal wclass is isomorphic to a wreath product of some transformation semigroup with some small category.
Abstract: We define the notion of a w-class of semigroups and prove that every endomorphism semigroup of a free product of semigroups from a maximal w-class is isomorphic to a wreath product of a transformation semigroup with some small category.
3 citations
3 citations
TL;DR: In this paper, it was shown that on a regular semigroup 5, the relation E restricted to RC(5) is a congruence and a characterisation of the greatest element of each E-class has been presented.
Abstract: If S is an inverse semigroup then E is a congruence on C(S). If S is a regular semigroup then each E -class of C(5) is a complete modular sublattice of C(5). (See [6]. ) In [5, Sec. 3] Petrich presents a few characterisations of E when S is an inverse semigroup. Here we prove that on a regular semigroup 5, the relation E restricted to RC(5) is a congruence. Also we extend Petrichfs results to the lattice RC(S) of a regular semigroup 5 and present a characterisation of the greatest element of each E-class. Characterisations of the least element of each E-class have been presented by Feigenbaum [I] and La Torte[4]. THE LATTICE RC(S) We use, whenever possible, the notation of Howie [3]. Recall first that a regular semigroup 5 is said to be R-u_~potent if its set of idempotents E(S) is a left reqular band, i.e. if E(5) satisfies the identity ere = el. In [7,1; 8, 1.1 ] it is shown that on a regular semigroup 5,
3 citations
TL;DR: This work stems from Weeg's [10], who considered a similar problem in the discrete case, and a conjecture of Weeg [10, p. 264] is resolved in the negative.
Abstract: In this paper, we consider the problem of what topological semigroups can serve as input semigroups of what (topological) automata. A semigroup is said to be admissible if it serves as an input semigroup of a non-trivial “strongly connected” automaton that has a distinguishable state (see Definition 2). For the discrete or the compact case, the class of all the admissible semigroups is fully characterized: a discrete or compact topological semigroup (I, m) is admissible if and only if there exists a closed congruence relationR such that the quotient semigroup (I/R, m R ) is non-trivial, right simple, and left unital. This work stems from Weeg's [10], who considered a similar problem in the discrete case.
3 citations