On maximal ideals of pseudo-BCK-algebras
We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.
We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.
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.
The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
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.