arXiv subjects
Publications and source records attributed to Susmita Mallick.
In this article, we concurrently explore the class of m-bi-ideals as well as the class of m- interior ideals in an ordered semigroup. We call these class of ideals as m-bi-interior ideals. Here, m-simple, m-regular ordered semigroups and their various subclasses get characterized in diverse manners as per their m-bi-interior ideals.
In this paper we characterize left(right) ideals, bi-ideals and quasi-ideals of an ordered semigroup by an index $m$ and give some important interplays between these ideals. The concept of m-regularity of an ordered semigroups has been introduced. Moreover m-regular ordered semigroups are characterized by their m-quasi-ideals and the fact that for any m-regular ordered semigroups $A$, the set $Q_{A}$ of all m-quasi-ideals of $A$, with multiplication defined by: $Q_{1}\circ Q_{2}=(Q_{1}Q_{2}]$, for all $Q_{1},Q_{2}\in Q_{A}$, is a m-regular semigroup is obtained here.
Following G.Szasz [2] a subsemigroup I of semigroup S is called an interior ideal if SIS \subset I. In this paper we explore the classes of regular semigroup and its different subclasses by their interior ideals. Furthermore, we introduce the strongly prime, prime, semiprime, strongly irreducible, and irreducible interior ideals of semigroups and also characterize those semigroups for which each interior ideal is strongly prime. Some important interplay between the classes of all interior ideals and other ideals are given here. In addition to this, we present different characterizations of semigroups by their minimal interior ideals.