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On pseudo BE-algebras

100%

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

Discussiones Mathematicae - General Algebra and Applications

2013

tom 33

nr 1

95-108

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 pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.

On normal filters and congruence relations in BE-algebras

88%

Walendziak A.

Commentationes Mathematicae

2012

tom 52

nr 2

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 filters in A ). Moreover, we give the construction of quotient algebra A/F of A via a normal filter F of A.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Discussiones Mathematicae - General Algebra and Applications

1 Ameri R.

1 Borzooei R.

1 Radfar A.

1 Rezaei A.

1 Saeid A.

1 Walendziak A.

1 2013

1 2012

Wyniki wyszukiwania

On pseudo BE-algebras

On normal filters and congruence relations in BE-algebras