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1
Content available remote Some properties of pseudo-BCI algebras
Dymek G.
Commentationes Mathematicae
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2018
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Vol. 58, No. 1/2
19--35
EN
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.
2
Content available remote Soft set theory applied to general algebras
Dymek G., Walendziak A.
Demonstratio Mathematica
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2015
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Vol. 48, nr 1
13--20
EN
The notions of a soft general algebra and a soft subalgebra are introduced and studied. The operations on them such as a restricted intersection, an extended intersection, a restricted union, a ^-intersection, a ˅-union and a cartesian product are established.
3
Content available remote On irreducible and prime deductive systems of pseudo-BCI-algebras
Dymek G.
Commentationes Mathematicae
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2014
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Vol 54, No. 1
67--78
4
Content available remote On the category of pseudo-BCI-algebras
Dymek G.
Demonstratio Mathematica
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2013
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Vol. 46, nr 4
631--644
EN
The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.
5
Content available remote Fuzzy ideals of pseudo-BCK algebras
Dymek G., Walendziak A.
Demonstratio Mathematica
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2012
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Vol. 45, nr 1
1-15
EN
Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set ž, the least fuzzy ideal containing ž is constructed. The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras in terms of fuzzy ideals are given.
6
Content available remote Atoms and ideals of pseudo-BCI-algebras
Dymek G.
Commentationes Mathematicae
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2012
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Vol. 52, [Z] 1
73-90
EN
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 At(X) of atoms of a pseudo-BCI-algebra X to be an ideal of X are established.
7
Content available remote Normal pseudo-BCK-algebras
Dymek G.
Commentationes Mathematicae
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2011
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Vol. 51, [Z] 1
99-107
EN
A normal pseudo-BCK-algebra X is an algebra in which every subalgebra of X is an ideal of X. Characterizations of normal pseudo-BCK-algebras are given.
8
Content available remote On maximal ideals of pseudo MV-algebras
Dymek G., Walendziak A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 1
117-126
9
Content available remote Fuzzy maximal ideals of pseudo MV-algebras
Dymek G.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2007
|
Vol. 47, [Z] 1
31-46
EN
The notion of fuzzy maximal ideals of a pseudo MV-algebra is introduced, and its characterizations are established.
10
Content available remote Cohomotopical admissibility and inverse limits
Dymek G., Prusiński A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 3
267-271
EN
The aim of this paper is to prove that if X = [formula] and all spaces Xα are n-cohomotopically admissible compacta then X is n-cohomotopically admissible i.e. n-cohomotopical admissibility is a continuous property under inverse limits. The idea of this proof is taken from [2]. Readers should be familiar with [2] and Section 2 of [3].
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