We show that for two partially ordered semigroups S and T with common local units, there exists a unitary Morita context with surjective maps if and only if the categories of closed right Sand T posets are equivalent.

In this paper we give a new proof of the following result of Straubing and Thérien: every J -trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1. We will assume in this paper that the reader has a basic background in finite semigroup theory (in particular, Green’s relations and identities defining varieties) and in computer science (languages, trees, heaps). All semi...

In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...

We consider the intuitionistic fuzzification of the concept of several ideals in an ordered semigroup S, and investigate some properties of such ideals. Mathematics Subject Classification: 06F35, 03G25, 03E72

The notion of intuitionistic fuzzy ideals with thresholds of an ordered semigroup is considered and some of its properties are given. An embedding theorem of the set of all intuitionistic fuzzy ideals with thresholds is presented and the homomorphic images and inverse images of intuitionistic fuzzy ideals with thresholds are studied too. 2010 Mathematics Subject Classification: 06F05

Let K be an anti-ideal of a semigroup (S,=, =, ·, θ) with apartness. A construction of the anti-congruence Q(K) and the quasi-antiorder θ, generated by K, are presented. Besides, a construction of the anti-order relation Θ on syntactic semigroup S/Q(K), generated by θ, is given in Bishop’s constructive mathematics.

Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an ( , )-fuzzy filter of an ordered semigroup , where , , , , with . Since the concept of ( , )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter,...

We introduce the notion of a sturdy frame of abstract algebras which is a common generalization of a sturdy semilattice of semigroups, the sum of lattice ordered systems, the strong distributive lattice of semirings, the sturdy frame of type (2, 2) algebras and the strong b-lattice of semirings. Also, we give some properties and characterizations of the sturdy frame of abstract algebras. As an ...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...