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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1193,
author = {Rajab Ali Borzooei and Arsham Borumand Saeid and Akbar Rezaei and Akefe Radfar and Reza Ameri},
title = {On pseudo BE-algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {33},
year = {2013},
pages = {95-108},
zbl = {1305.06020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1193}
}
Rajab Ali Borzooei; Arsham Borumand Saeid; Akbar Rezaei; Akefe Radfar; Reza Ameri. On pseudo BE-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 33 (2013) pp. 95-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1193/
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