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Semitopological BL-algebras and MV-algebras

100%

Zahiri O. , Borzooei R. A.

Demonstratio Mathematica

2014

tom Vol. 47, nr 3

522--538

In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology γx on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV-algebra by using two kinds of definition of MV–algebra and show that they are equivalent.

Involutory BE-algebras

80%

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

Journal of Mathematics and Applications

2014

tom 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.

Distributive pseudo BE-algebras

70%

Borzooei R. A. , Saeid A. B. , Rezaei A. , Radfar A. , Ameri R.

Fasciculi Mathematici

2015

tom Nr 54

21--39

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.