We determine all periodic (and, therefore, all finite) semigroups G for which there exists a non-empty subset S of G such that the Cayley graph of G relative to S is an undirected Cayley graph. Let G be a semigroup, and let S be a nonempty subset of G. The Cayley graph Cay(G,S) of G relative to S is defined as the graph with vertex set G and edge set E(S) consisting of those ordered pairs (x, y...

We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which are necessary to make the problem well defined, the uniform word problem for semigroups described by automatic structures is decidable. Under the same conditions, we show that one can also ...

A numerical index is introduced for semigroups of completely positive maps of B(H) which generalizes the index of E0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E0-semigroup, provided that the dilation is minimal. Introduction. We introduce a numerical index for semigroups P = {Pt : t ≥ 0} of normal completely posi...

The free product CR S i of an arbitrary family of disjoint completely simple semigroups fS i g i2I , within the variety CR of completely regular semigroups, is described by means of a theorem generalizing that of Ka dourek and Poll ak for free completely regular semigroups. A notable consequence of the description is that all maximal subgroups of CR S i are free, except for those in the factors...

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

We call (T (t))t≥0 an abstract delay semigroup. This notion is introduced in more detail in Section 2. The semigroup thus obtained is rarely a contraction semigroup. In this paper we will show that under very mild conditions, we may change the inner product on E into an equivalent inner product, such that the delay semigroup becomes a (generalized) contraction semigroup. A contraction semigroup...

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

Let S be a semigroup. For a, x ∈ S such that a = axa, we say that x is an associate of a. A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S. It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose H -relation is a...