We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α 7→ α, where α is the identity map on the domain of α. We investigate t...

In theory of topological LA-semigroups, we introduce the concepts LA-loop functions for LA-lifting in LA-fibrations. We prove that function and any LA-fibration are not necessarily unique. also restrict on idempotent point LA-fiber space to get another LA-map which is called a restriction.

We introduce semigroups of dominoes as a tool for working with sets of linked strings. In particular, we are interested in splicing semigroups of dominoes. In the special case of alphabetic (symbol-to-symbol linked) dominoes the splicing semigroups are essentially equivalent to the splicing systems introduced by Head to study infor-mational macromolecules, speciically to study the eeect of sets...

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...

We investigate the complexity of deciding, given a multiplication table representing a semigroup S, a subset X of S and an element t of S, whether t can be expressed as a product of elements of X. It is well-known that this problem is NL-complete and that the more general Cayley groupoid membership problem, where the multiplication table is not required to be associative, is P-complete. For gro...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza's theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford's work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

In this paper, we study the complete ⋆-metric semigroups and groups Raǐkov completion of invariant groups. We obtain following. (1) Let (X,d⋆) be a space containing semigroup (group) G that is dense subset X. If restriction d⋆ on invariant, then X can become as subgroup, (2) (G,d⋆) group such G. Then, if only (G,τd⋆) complete.