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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.

On pseudo-bci ideals of pseudo-bci algebras

Young Bae Jun, Hee Sik Kim, J. Neggers (2006)

Matematički Vesnik

On pseudo-BCI-algebras

Grzegorz Dymek (2015)

Annales UMCS, Mathematica

The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.

On $Q$ -algebras.

Neggers, Joseph, Ahn, Sun Shin, Kim, Hee Sik (2001)

International Journal of Mathematics and Mathematical Sciences

On ( $\in, \in \lor q$ )-fuzzy filters of pseudo-BL algebras.

Zhan, Jianming, Jun, Young Bae, Dudek, Wiesław A. (2010)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On sensible fuzzy ideals of BCK-algebras with respect to a t-conorm.

Akram, M., Zhan, Jianming (2006)

International Journal of Mathematics and Mathematical Sciences

On some classes of BCH-algebras.

Chaudhry, Muhammad Anwar, Fakhar-Ud-Din, Hafiz (2001)

International Journal of Mathematics and Mathematical Sciences

On the class of QS-algebras.

Kondo, Michiro (2004)

International Journal of Mathematics and Mathematical Sciences

On the degrees of permutability of subregular varieties

Graham D. Barbour, James G. Raftery (1997)

Czechoslovak Mathematical Journal

On two classes of pseudo-BCI-algebras

Grzegorz Dymek (2011)

Discussiones Mathematicae - General Algebra and Applications

The class of p-semisimple pseudo-BCI-algebras and the class of branchwise commutative pseudo-BCI-algebras are studied. It is proved that they form varieties. Some congruence properties of these varieties are displayed.

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