Distributive Pseudo Be-Algebras (original) (raw)
Discussiones Mathematicae - General Algebra and Applications, 2013
In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and preimage of a pseudo filter is also a pseudo filter. Furthermore, the notion 96 R.A. Borzooei, A.
Some New Results on BE-Algebras
Pan-American journal of mathematics, 2024
Then this class of logical algebras was the focus of many researchers. In this paper, the concept of atoms in BE-algebras is introduced and analyzed, and, in addition, it is directly connected to two-membered BE-filters. A criterion was found for determining the existence of atoms in these algebras. In addition to the previous one, the paper designs two types of BE-algebra extensions by adding one element so that the additional element is an atom in it. In addition to the previous one, two new types of filters in BE-algebras are designed.
Fuzzy filters of pseudo-BE algebras
Afrika Matematika, 2019
The theory of fuzzy filters in pseudo-BE algebras is developed. Various characterizations of fuzzy filters are given. It is proved that the set of all fuzzy filters of a pseudo-BE algebra is a complete lattice. Some characterizations of Noetherian pseudo-BE algebras by fuzzy filters are obtained. Finally, fuzzy commutative filters are defined and studied. Moreover, the homomorphic properties of fuzzy (commutative) filters are provided.
• Dual Psuedo-Complemented Almost Distributive Lattices
International Journal of Mathematical Archive, 2012
The concept of a dual pseudo-complemented Almost Distributive Lattice is introduced. Necessary and sufficient conditions for an Almost Distributive Lattice to become a dual pseudo-complemented Almost Distributive Lattice are derived. It is proved that a dual pseudo-complemented Almost Distributive Lattice is equationally definable. A one to one correspondence between the set of all dual pseudo-complementations on an ADL and the set of all maximal elements of is obtained. Also proved that the set is a Boolean algebra.
Fuzzy Medial Filters of Pseudo Be-Algebras
2021
In this paper, the notion of fuzzy medial filters of a pseudo BE-algebra is defined, and some of the properties are investigated. We show that the set of all fuzzy medial filters of a pseudo BE-algebra is a complete lattice. Moreover, we state that in commutative pseudo BE-algebras fuzzy filters and fuzzy medial filters coincide. Finally, the notion of a fuzzy implicative filter is introduced and proved that every fuzzy implicative filter is a fuzzy medial filter, and we show that the converse is not valid in general.
Filters and ideals in pseudocomplemented posets
2022
We study ideals and filters of posets and of pseudocomplemented posets and show a version of the Separation Theorem, known for ideals and filters in lattices and semilattices, within this general setting. We extend the concept of a *-ideal already introduced by Rao for pseudocomplemented distributive lattices and by Talukder, Chakraborty and Begum for pseudocomplemented semilattices to pseudocomplemented posets. We derive several important properties of such ideals. Especially, we explain connections between prime filters, ultrafilters, filters satisfying the *-condition and dense elements. Finally, we prove a Separation Theorem for *-ideals.
A note on certain filters, ideals and essences in BE-algebra
AIP Conference Proceedings
In this paper we want to introduce the idea of Cartesian product of BE-algebras. The concept plays a significant role in the study of BE-algebras. Furthermore we continue to study the Cartesian product of filters, ideals and essences in BE-algebra with some characteristic properties.
Filters and congruences in sectionally pseudocomplemented lattices and posets
Soft Computing
Together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that—similar to relatively pseudocomplemented lattices—these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters in both sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e., ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined.