Search results for: Andrzej Walendziak

Items from 1 to 20 out of 24 results

article

The p-semisimple property for some generalizations of BCI algebras and its applications

Lidia Obojska, Andrzej Walendziak

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2020 > 19 > 79-94

This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.

article

The property of commutativity for some generalizations of BCK algebras

Andrzej Walendziak

Soft Computing > 2019 > 23 > 17 > 7505-7511

We consider thirty generalizations of BCK algebras (RM, RML, BCH, BCC, BZ, BCI algebras and many others). We investigate the property of commutativity for these algebras. We also give 10 examples of proper commutative finite algebras. Moreover, we review some natural classes of commutative RML algebras and prove that they are equationally definable.

article

Pseudo-BCH Semilattices

Andrzej Walendziak

Bulletin of the Section of Logic > 2018 > 47 > 2

In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition,...

article

Some results on pseudo-Q algebras

Akbar Rezaei, Arsham Borumand Saeid, Andrzej Walendziak

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2017 > 16

The notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.

article

On branchwise commutative pseudo-BCH algebras

Andrzej Walendziak

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica > 2017 > 71 > 2

Basic properties of branches of pseudo-BCH algebras are described. Next, the concept of a branchwise commutative pseudo-BCH algebra is introduced. Some conditions equivalent to branchwise commutativity are given. It is proved that every branchwise commutative pseudo-BCH algebra is a pseudo-BCI algebra.

article

Strong ideals and horizontal ideals in pseudo-BCH-algebras

Andrzej Walendziak

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2016 > 15

In this paper we define strong ideals and horizontal ideals in pseudo-BCH-algebras and investigate the properties and characterizations of them.

article

On ideals of pseudo-BCH-algebras

Andrzej Walendziak

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica > 2016 > 70 > 1

In this paper we introduce the notion of a disjoint union of pseudo-BCH-algebras and describe ideals in such algebras. We also investigate ideals of direct products of pseudo-BCH-algebras. Moreover, we establish conditions for the set of all minimal elements of a pseudo-BCH-algebra X to be an ideal of X.

article

Pseudo-BCH-algebras

Andrzej Walendziak

Discussiones Mathematicae - General Algebra and Applications > 2015 > 35 > 1 > 5-19

The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH-algebras are considered.

article

BM-Algebras and related topics

Andrzej Walendziak

Mathematica Slovaca > 2014 > 64 > 5 > 1075-1082

Some connections between BM-algebras and its related topics are studied. It is proved that the class of medial BH-algebras coincides with the class of BM-algebras. Moreover, the congruence lattice of a BM-algebra is investigated.

article

On implicative and maximal ideals of BL-algebras

Andrzej Walendziak

Commentationes Mathematicae > 2014 > 54 > 2

In the theory of MV-algebras, implicative ideals are studied by Hoo and Sessa. In this paper we define and characterize implicative ideals of BL-algebras. We also investigate maximal ideals of BL-algebras and prove that if an ideal is prime and implicative, then it is maximal. Moreover, we show that an ideal is maximal if and only if the quotient BL-algebra is a simple MV-algebra. Finally, we give...

article

Fuzzy filters of BE-algebras

Grzegorz Dymek, Andrzej Walendziak

Mathematica Slovaca > 2013 > 63 > 5 > 935-946

Characterizations of fuzzy filters in a BE-algebra are established. Conditions for a fuzzy set to be a fuzzy filter are given. For a fuzzy set µ the least fuzzy filter containing µ is constructed. The homomorphic properties of fuzzy filters of a BE-algebra are provided. Finally, characterizations of Noetherian BE-algebras and Artinian BE-algebras via fuzzy filters are obtained.

article

On complete pseudo-BL-algebras. A Cantor-Bernstein type theorem

Andrzej Walendziak, Magdalena Wojciechowska-Rysiawa

Mathematica Slovaca > 2012 > 62 > 5 > 815-828

Pseudo-BL-algebras are a noncommutative extention of BL-algebras. In this paper we consider polars in pseudo-BL-algebras and the class of complete pseudo-BL-algebras. In the final section, a version of the Cantor-Bernstein theorem will be proved.

article

On normal filters and congruence relations in BE-algebras

Andrzej Walendziak

Commentationes Mathematicae > 2012 > 52 > 2

In this paper we introduce the notion of a normal filter in BE-algebras (in transitive BE-algebras filters conicide with normal filters). We discuss some relationships between congruence relations and normal filters of a BE-algebra A (if A is commutative, then we show that there is a bijection between congruence relations and filters in A ). Moreover, we give the construction of quotient algebra A/F...

article

On maximal ideals of pseudo-BCK-algebras

Andrzej Walendziak

Discussiones Mathematicae - General Algebra and Applications > 2011 > 31 > 1 > 61-73

We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.

article

Some characterizations of pseudo-BL-chains

Andrzej Walendziak, Magdalena Wojciechowska-Rysiawa

Commentationes Mathematicae > 2011 > 51 > 2

Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.

article

Nontrivial BCK/BCI-algebras do not satisfy the fuzzy ascending chain condition

Andrzej Walendziak

Fuzzy Sets and Systems > 2007 > 158 > 8 > 922-923

In [J. Meng, X. Guo, On fuzzy ideals in BCK/BCI-algebras, Fuzzy Sets and Systems 149 (2005) 509–525], Meng and Guo gave some characterizations of Noetherian BCK/BCI-algebras by fuzzy ideals. They introduced (see Definition 6.2) the notion of the fuzzy ascending chain condition (briefly, FACC) and stated that a BCK/BCI-algebra X is Noetherian if and only if X satisfies the FACC (Theorem 6.5), but it...

article

On BF-algebras

Andrzej Walendziak

Mathematica Slovaca > 2007 > 57 > 2 > 119-128

In this paper we introduce the notion of BF-algebras, which is a generalization of B-algebras. We also introduce the notions of an ideal and a normal ideal in BF-algebras. We investigate the properties and characterizations of them.

article

On maximal ideals of pseudo \(MV\)-algebras

Grzegorz Dymek, Andrzej Walendziak

Commentationes Mathematicae > 2007 > 47 > 1

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.

article

Subalgebras and Homomorphic Images of Algebras Having the CEP and the WCIP

Andrzej Walendziak

Czechoslovak Mathematical Journal > 2004 > 54 > 1 > 155-160

In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with...

article

Relations Between Some Dimensions of Semimodular Lattices

Andrzej Walendziak

Czechoslovak Mathematical Journal > 2004 > 54 > 1 > 73-77

The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiński and Puczyłowski.

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(PSEUDO-)BCK/BCI/BCH-ALGEBRA (4)
CENTRE (3)
IDEAL (3)
(PSEUDO-)BCK/BCI/BCH ALGEBRA (2)
ARITHMETICAL AT 1 (2)
BE-ALGEBRA (2)
CEP (2)
LATTICE (2)
PSEUDO-BCH JOIN (MEET)-SEMILATTICE (2)
SEMIMODULAR LATTICE (2)
WCIP (2)
WEAK CONGRUENCE (2)
WEAKLY REGULAR (2)
BF/BF 1/BF 2-ALGEBRA (1)
BG-ALGEBRA (1)
BH-ALGEBRA (1)
(ASSOCIATIVE) BM-ALGEBRA (1)
(CLOSED) IDEAL (1)
(COMMUTATIVE) PSEUDO-CI/BE ALGEBRA (1)
(DUAL) PSEUDO-BCH ALGEBRA (1)
(MAXIMAL) IDEAL (1)
(MEDIAL) BH/BRK/BCH/BCI/BG/BF/B-ALGEBRA (1)
(NORMAL) FILTER (1)
3G25 (1)
6A12 (1)
6F35 (1)
ANTISYMMETRY (1)
ATOM (1)
BCK/BCI-ALGEBRA (1)
BL-ALGEBRA, MV-ALGEBRA, IMPLICATIVE (MAXIMAL) IDEAL (1)
BRANCH (1)
BRANCHWISE COMMUTATIVITY (1)
CANTOR-BERNSTEIN THEOREM (1)
CLOSED IDEAL (1)
COMMUTATIVE BE-ALGEBRA (1)
COMMUTATIVITY (1)
COMPLEMENTED LATTICE (1)
COMPLETE PSEUDO-BL-ALGEBRA (1)
CONGRUENCE PERMUTABLE (1)
CONGRUENCE RELATION (1)
DISJOINT UNION (1)
DUAL PSEUDO-Q/QC ALGEBRA (1)
EQUATIONAL CLASS (1)
FILTER (1)
FUZZY FILTER (1)
FUZZY IDEAL (1)
GOLDIE DIMENSION (1)
HOLLOW DIMENSION (1)
HORIZONTAL IDEAL (1)
JOIN IRREDUCIBLE ELEMENT (1)
KUROSH-ORE DIMENSION (1)
MAXIMAL (IMPLICATIVE) IDEAL (1)
MEREOLOGY (1)
MINIMAL ELEMENT (1)
NOETHERIAN (ARTINIAN) BE-ALGEBRA (1)
NORMAL IDEAL (1)
P-SEMISIMPLICITY (1)
POLAR (1)
PSEUDO MV-ALGEBRA (1)
PSEUDO-BCI/BCK ALGEBRA (1)
PSEUDO-BCK-ALGEBRA (1)
PSEUDO-BL-ALGEBRA (1)
PSEUDO-BL-ALGEBRA (-CHAIN) (1)
QUASI-BCK* ALGEBRA (1)
QUOTIENT BF-ALGEBRA (1)
RM, RML, BCH, BCC, BZ, BCI ALGEBRA (1)
RM/TRM/*RM/RM**/*ARM/BCI/BCH/BZ/PRE-BZ/PRE-BCI ALGEBRAS (1)
STONE LATTICE (1)
STRONG IDEAL (1)
SUBALGEBRA (1)
TRANSITIVE BE-ALGEBRA (1)
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Springer (9)
CEJSH (1)
Elsevier (1)
PSJD (1)

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Search results for: Andrzej Walendziak

The p-semisimple property for some generalizations of BCI algebras and its applications

The property of commutativity for some generalizations of BCK algebras

Pseudo-BCH Semilattices

Some results on pseudo-Q algebras

On branchwise commutative pseudo-BCH algebras

Strong ideals and horizontal ideals in pseudo-BCH-algebras

On ideals of pseudo-BCH-algebras

Pseudo-BCH-algebras

BM-Algebras and related topics

On implicative and maximal ideals of BL-algebras

Fuzzy filters of BE-algebras

On complete pseudo-BL-algebras. A Cantor-Bernstein type theorem

On normal filters and congruence relations in BE-algebras

On maximal ideals of pseudo-BCK-algebras

Some characterizations of pseudo-BL-chains

Nontrivial BCK/BCI-algebras do not satisfy the fuzzy ascending chain condition

On BF-algebras

On maximal ideals of pseudo \(MV\)-algebras

Subalgebras and Homomorphic Images of Algebras Having the CEP and the WCIP

Relations Between Some Dimensions of Semimodular Lattices

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