(Skew) Filters in Residuated Skew Lattices

In this paper, we show the relationship between (skew) deductive system and (skew) filter in residuated skew lattices. It is shown that if a residuated skew lattice is conormal, then any skew deductive system is a skew filter under a condition and deductive system and skew deductive system are equivalent under some conditions too. It is investigated that in branchwise residuated skew lattice, filter, deductive system and skew deductive system are equivalent. We define some types of prime (skew) filters in residuated skew lattices and show the relationship between prime (skew) filters and residuated skew chaines. It is proved that in prelinear residuated skew lattice any proper filter can be extended to a maximal, prime filter of type (I). The notion of the radical of a filter is defined and several characterizations of the radical of a filter are given. We show that in non conormal prelinear residuated skew lattice with element 0, infinitesimal elements are equal to intersection of all the maximal filters

Some properties of residual mapping and convexity in ∧-hyperlattices

The aime of this paper is the study of residual mappings and convexity in hyperlattices. To get this point, we study principal down set in hyperlattices and we give some conditions for a mapping between two hyperlattices to be equivalent with a residual maping. Also, we investigate convex subsets in ∧-hyperlattices

Multiplier in BL-algebras

Abstract In this paper, we introduce the notion of multiplier in -algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and ( , -derivations in -algebras. We introduce the concept of idempotent multipliers in BL-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. Also, we introduce the special multiplier and study some properties. Finally, we show that if is a boolean algebra, then the set of all multipliers of is a -algebra under some conditions

Extensions of BCK-algebras

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the notion of BCI/BCK-algebras. This structure is studied in detail. Also we introduce a way to make an eBCK-algebra from a BCK-algebra and vice versa