On ordered regular semigroups with biggest inverses.
In this paper we prove a theorem of Cantor-Bernstein type for orthogonally -complete lattice ordered groups.
We show that given infinite sets and a function which is onto and -to-one for some , the preimage of any ultrafilter of under extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model with a set of atoms and a finite-to-one onto function such that for each free ultrafilter of its preimage under does not extend to an ultrafilter. In addition, we show that in there exists an ultrafilter compact pseudometric...
In this paper we apply the notion of the product -algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an -algebra into a product -algebra. We found sufficient conditions under which any two direct product decompositions of a product -algebra have isomorphic refinements.
In this paper a combinatorial result concerning paire of projective intervals of a modular lattice will be established.
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.