In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the related relation defined on this structure is transitive and prove that every pseudo upper set is a pseudo filter. Also, the pseudo filter generated by a set is define and show that the set of all pseudo filters is distributive complete lattice but it is not complemented. the notion of prime and irreducible subset and prove that every irreducible subset is prime.
In this paper, we introduce a new algebra, called a BI-algebra, which is a generalization of a (dual) implication algebra and we discuss the basic properties of BI-algebras, and investigate ideals and congruence relations.
In this paper the notion of fuzzy B E-algebras are introduced. We state and prove some theorems in fuzzy B E-algebras and level subalgebras. Some characterizations of fuzzy subalgebras of B E-algebras are given. Using fuzzy subalgebras, characterizations of Artinian and Noetherian B E-algebras are also established. Finally the notion of fuzzy topological B E-algebras is introduced. We state and prove the Foster's results on homomorphic images and inverse images in fuzzy topological B E-algebras.
In this paper we study properties of commutative BE-algebras and we give the construction of quotient (X/I; * , I) of a commutative BE-algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we define and study commutative ideals in BE-algebras.
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