Geodesic
On pseudo BE-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 95-108

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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.
Keywords: BE-algebra, Pseudo BE-algebra, pseudo filter, pseudo upper set 
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Borzooei, Rajab; Saeid, Arsham; Rezaei, Akbar; Radfar, Akefe; Ameri, Reza. On pseudo BE-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 33 (2013) no. 1, pp. 95-108. http://geodesic.mathdoc.fr/item/DMGAA_2013_33_1_a6/