We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p, q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p, q). On the other hand, we construct a consistent example of a Tychonov countably compact semigroup containing a copy of C(p, q). In this paper we study the structural prope...

In the paper we study (countably) compact and (absolutely) H-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup. In this paper all spaces are Hausdorff. A semigr...

A semigroup whose bi-ideals and quasi-ideals coincide is called a -semigroup. The full transformation semigroup on a set X and the semigroup of all linear transformations of a vector space V over a field F into itself are denoted, respectively, by T(X) and LF(V). It is known that every regular semigroup is a -semigroup. Then both T(X) and LF(V) are -semigroups. In 1966, Magill introduced and st...

It is known that a regularly Lyapounov function for a semigroup of contractions on a Hilbert space converges to its minimum along the trajectories of the semigroup. In this paper we show that this Lyapounov function nearly converges to its minimum along trajectories of the semigroup generated by a small bounded perturbation of the semigroup generator.

The aim of this paper is to apply the concept of fuzzy soft sets over a Γ -semigroup. Here the notion of fuzzy soft ideals over a Γ -semigroup has been introduced. The special union, intersection and product of fuzzy soft ideals over a Γ -semigroup have been defined and proved that these are also fuzzy soft Γ -ideals over the Γ -semigroup.

in this paper we establish a characterization of abelian compact hausdorff semigroups with unique idempotent and ideal retraction property. we also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

in this paper we introduce and study an algebraic structure, namely grouplike. a grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). the first idea of grouplikes comes from b-parts and $b$-addition of real number...

The notion of a &Gamma-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a &Gamma-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered &Gamma-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered &Gamma- semigroups analogous to the charact...

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 ...

Semigroups whose congruences form a chain are often termed ∆-semigroups. The commutative ∆-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative ∆-semigroups. It turns out that there are only six noncommutative exampl...