Results

**1 - 2**of**2**### ON COMMUTATIVE HYPER BE-ALGEBRAS

"... Abstract. In this paper, we introduce commutative hyper BE-algebra and study it in detail. We show that every commutative (row diagonal, column row, very thin) hyper BE-algebra is a BE-algebra. ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. In this paper, we introduce commutative hyper BE-algebra and study it in detail. We show that every commutative (row diagonal, column row, very thin) hyper BE-algebra is a BE-algebra.

### COMMUTATIVE PSEUDO BE-ALGEBRAS

, 2016

"... Abstract. The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties. We generalize some results proved by A. Walendziak for the case of commutative BE-algebras. We prove that the class of commutative pseudo BE-algebras is equivalent to the c ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties. We generalize some results proved by A. Walendziak for the case of commutative BE-algebras. We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-algebras also hold for commutative pseudo BE-algebras. For example, any finite commutative pseudo BE-algebra is a BE-algebra, and any commutative pseudo BE-algebra is a join-semilattice. Moreover, if a commutative pseudo BE-algebra is a meet-semilattice, then it is a distributive lattice. We define the pointed pseudo-BE algebras, and introduce and study the relative negations on pointed pseudo BE-algebras. Based on the relative negations we construct two closure operators on a pseudo BE-algebra. We also define relative involutive pseudo BE-algebras, we investigate their properties and prove equivalent conditions for a relative involutive pseudo BEalgebra. We define the relative Glivenko property for a relative good pseudo BE-algebra and show that any relative involutive pseudo BE-algebra has the relative Glivenko property.