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On pseudo BE-algebras

Rajab Ali BorzooeiArsham Borumand SaeidAkbar RezaeiAkefe RadfarReza Ameri — 2013

Discussiones Mathematicae - General Algebra and Applications

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.

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