We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

Fountain and Gomes have shown that any proper left ample semigroup embeds into a so-calledW -product, which is a subsemigroup of a reversed semidirect product T ⋉ Y of a semilattice Y by a monoid T , where the action of T on Y is injective with images of the action being order ideals of Y. Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim o...

in the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(s) is the dual of a function algebra.

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 ...

Each factor semigroup of a free restriction (ample) semigroup over a congruence contained in the least cancellative congruence is proved to be embeddable into a W -product of a semilattice by a monoid. Consequently, it is established that each restriction semigroup has a proper (ample) cover embeddable into such a W -product.

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

Fountain and Gomes have shown that any proper left ample semigroup embeds into a so-called W -product, which is a subsemigroup of a reverse semidirect product T ⋉ Y of a semilattice Y by a monoid T , where the action of T on Y is injective with images of the action being order ideals of Y. Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim o...

Dempster-Shafer theory is one of the main tools for reasoning about data obtained from multiple sources, subject to uncertain information. In this work abstract algebraic properties of the Dempster-Shafer set of mass assignments are investigated and compared with the properties of the Bayes set of probabilities. The Bayes set is a special case of the Dempster-Shafer set, where all non-singleton...

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.