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Involutory BE-algebras

Borzooei R. A., Borumand Saeid A., Ameri R., Rezaei A.

Journal of Mathematics and Applications

2014

Vol. 37

13--26

This paper is devoted to the study of some structural properties of bounded and involutory BE-algebras and investigate the relationship between them. We construct a commutative monoid by definition of proper operation in an involutory BE-algebra. Some rules of calculus for BE-algebras with a semi-lattice structure are provided. Many results related to the natural order of a BE-algebras were found. Finally, we show that an involutory bounded BE-algebra X is semi-simple.

On normal niters and congruence relations in BE-algebras

Walendziak A.

Commentationes Mathematicae

2012

Vol. 52, [Z] 2

199--205

In this paper we introduce the notion of a normal filter in BE-algebras (in transitive BE-algebras filters conicide with normal filters). We discuss some relationships between congruence relations and normal filters of a BE-algebra A (if A is commutative, then we show that there is a bijection between congruence relations and niters in A). Moreover, we give the construction of quotient algebra A/F of A via a normal filter F of A.