In this paper, we study the Morita context for arbitrary semigroups. We prove that, for two semigroups S and T, if there exists a Morita context (S, T, P,Q, τ, μ) (not necessary unital) such that the maps τ and μ are surjective, the categories US-FAct and UT -FAct are equivalent. Using this result, we generalize Theorem 2 in [2] to arbitrary semigroups. Finally, we give a characterization of Mo...

In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left ...

After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I n λ of the rank 6 n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. W...

Munn’s construction of a fundamental inverse semigroup TE from a semilattice E provides an important tool in the study of inverse semigroups. We present here a semigroup FE that plays for a class of E-semiadequate semigroups the role that TE plays for inverse semigroups. Every inverse semigroup with semilattice of idempotents E is E-semiadequate. There are however many interesting E-semiadequat...

Semigroups with an additional unary operation called a (right) closure are investigated. These “closure semigroups” may be viewed as (not necessarily regular) generalisations of inverse semigroups, and several powerful structural aspects of inverse semigroup theory are shown to extend naturally to some important classes of closure semigroups. These include representations as partial transformat...

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. the purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. to provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

The syntactic complexity of a regular language is the size of its syntactic semigroup. This semigroup is isomorphic to the transition semigroup of the minimal deterministic finite automaton accepting the language, that is, to the semigroup generated by transformations induced by non-empty words on the set of states of the automaton. In this paper we search for the largest syntactic semigroup of...

In this paper we develop an analog of the notion of the con- jugacy graph of  nite groups for the  nite semigroups by considering the Green relations of a  nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a  nite semigroup S , we  first atte...