On pseudo-BCI-algebras
The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
Noetherian and Artinian pseudo MV-algebras
The notions of Noetherian pseudo MV-algebras and Artinian pseudo MV-algebras are introduced and their characterizations are established. Characterizations of them via fuzzy ideals are also given.
Bipartite pseudo MV-algebras
A bipartite pseudo MV-algebra A is a pseudo MV-algebra such that A = M ∪ M ̃ for some proper ideal M of A. This class of pseudo MV-algebras, denoted BP, is investigated. The class of pseudo MV-algebras A such that A = M ∪ M ̃ for all maximal ideals M of A, denoted BP₀, is also studied and characterized.
On a period of elements of pseudo-BCI-algebras
The notions of a period of an element of a pseudo-BCI-algebra and a periodic pseudo-BCI-algebra are defined. Some of their properties and characterizations are given.
On two classes of pseudo-BCI-algebras
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.
On fuzzy ideals of pseudo MV-algebras
Fuzzy ideals of pseudo MV-algebras are investigated. The homomorphic properties of fuzzy prime ideals are given. A one-to-one correspondence between the set of maximal ideals and the set of fuzzy maximal ideals μ satisfying μ(0) = 1 and μ(1) = 0 is obtained.
On a periodic part of pseudo-BCI-algebras
In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.
On pseudo-BCI-algebras
The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
Normal pseudo-BCK-algebras
A normal pseudo-BCK-algebra is an algebra in which every subalgebra of is an ideal of . Characterizations of normal pseudo-BCK-algebras are given.
Atoms and ideals of pseudo-BCI-algebras
The main subject of the paper are atoms and ideals of a pseudo-BCI-algebra. Many different characterizations of them are given. Some connections between ideals and subalgebras are presented. Conditions for the set of atoms of a pseudo-BCI-algebra to be an ideal of are established.
On irreducible and prime deductive systems of pseudo-BCI-algebras
Some properties of pseudo-BCI algebras
In this paper the notion of an essential closed deductive system of a pseudo-BCI algebra is defined and investigated. Among other things, it is proved that such a deductive system contains all coatoms of the pseudo-BCI algebra. Also, the notions of homomorphisms and semihomomorphisms of pseudo-BCI algebras are studied and some of their properties are presented.
Fuzzy maximal ideals of pseudo MV-algebras
The notion of fuzzy maximal ideals of a pseudo MV-algebra is introduced, and its characterizations are established.
On maximal ideals of pseudo -algebras
We investigate maximal ideals of pseudo MV-algebras and give some characterizations of them. Some properties of a family of maximal ideals of a pseudo MV-algebra generating this algebra are shown as well. Finally, we are interested in finding an example of a pseudo MV-algebra generated by its maximal ideal.
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