To every right or left Bol loop corresponds a middle loop. In this paper, the cores of loops (RBL) and its corresponding (MBL) were studied. Their algebraic connections considered. It was shown that core RBL is elastic idempotent. The found to be alternative (or idempotent) if only MBL symmetric. If (left) symmetric, then, medial (semimedial). has inverse property (automorphic property, idempot...

The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three twosided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an ω1-generated uniserial module over every non-artini...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S. Keywords—Ordered semigroup; ordered fuzzy point; weakly prime fuzzy left ideal; weakly ...

We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean combinations. These properties include effective algebraic characterizations and lattice identities. In the main part of this paper we consider the following determini...

In this paper we investigated some operations on fuzzy h-ideals. Among all the results, we show that the set of all fuzzy left h-ideals of a Γ−hemiring S is zerosumfree hemiring having infinite element 1 under the operations of sum and composition of fuzzy left h-ideals of S. Mathematics Subject Classification: 08A72,16Y99

Using the notion of an anti fuzzy point and its besideness to and non-quasicoincidence with a fuzzy subset, some new concept of an anti fuzzy interior ideals in LA-semigroups are introduced and their interrelations and related properties are investigated. We also introduce the notion of a strongly besideness and strongly non-quasicoincidence of an anti fuzzy point with a fuzzy subset and charac...

In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. Key words: Intuitionistic fuzzy set; intuitionistic fuzzy bi-ideal; intuitionistic fuzzy prime (resp. strongly prime and semiprime) ...

In this paper, we introduce the notions of interval-valued fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each interval-valued fuzzy bi-ideal is semiprime and strongly prime.