‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduc...

The notions of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are introduced, and related properties are investigated. Characterizations of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are discussed. A regular semigroup is characterized by the notion of a uni-soft quasi ideal.

In this paper we introduced the notions of uni-soft AG-groupoids, uni-soft left(right) ideals and uni-soft quasi ideals of AG-groupoids and also investigated related properties of these structures. Some interesting Characterizations of uni-soft AG-groupoids and uni-soft left(right) ideals have been explored. Mathematics Subject Classification: 42B20, 42B25, 46E30

In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in re...

Uniication modulo the theory of Boolean algebras has been investigated by several autors. Nevertheless, the exact complexity of the decision problem for uniication with constants and general uniication was not known. In this research note, we show that the decision problem is p 2-complete for uniication with constants and PSPACE-complete for general uniication. In contrast, the decision problem...

In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Bool...