Papers by Andrzej Walendziak
We show that every pair of congruences on a BG-algebra (also on a BF1/B/BM-algebra) permutes. Thi... more We show that every pair of congruences on a BG-algebra (also on a BF1/B/BM-algebra) permutes. This result implies that if A is a BG/BF1/B/BM-algebra, then the lattice of all congruences on A is modular. Moreover, it is proved that BF-algebras and BCK-algebras (BCI/BCH/BH-algebras, too) are not congruence permutable, in general. Mathematics Subject Classi…cation: 06F35.
Soft Computing, 2018
We consider thirty generalizations of BCK algebras (RM, RML, BCH, BCC, BZ, BCI algebras and many ... more 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.
Communications in Algebra, 2000
Weak direct products of arbitrary universal algebras are investigated. Some applications to algeb... more Weak direct products of arbitrary universal algebras are investigated. Some applications to algebras whose congruences permute and to congruence distributive algebras are considered.
Discussiones Mathematicae - General Algebra and Applications, 2011
We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.
Portugaliae Mathematica, 1994
Any atomistic lattice is strong whereas the converse does not hold, in general. In the present pa... more Any atomistic lattice is strong whereas the converse does not hold, in general. In the present paper we prove that, if in a strong atomic J-lattice, each atom has a complement, then the lattice is atomistic. This result generalizes the theorem of [2].
J. Multiple Valued Log. Soft Comput., 2021
Algebra Universalis, 1997
Abstract. It is well-known that a finite lattice L is isomorphic to the lattice of flats of a mat... more Abstract. It is well-known that a finite lattice L is isomorphic to the lattice of flats of a matroid if and only if L is geometric. A result due to Edelman (see [1], Theorem 3.3) states that a lattice is meet-distributive if and only if it is isomorphic to the lattice of all closed sets of a convex geometry. In this note we prove that a finite lattice is the lattice of closed sets of a closure space with the Steinitz exchange property if and only if it is a consistent lattice.
Algebra Universalis, 2000
Abstract. In the present paper we characterize atomistic lattices. These characterizations are gi... more Abstract. In the present paper we characterize atomistic lattices. These characterizations are given in terms of concepts related to pure elements (cf. [4], [6]) and neat elements (cf. [3]).
The concept of normal subalgebras in B- algebras is due to J. Neggers and H. S. Kim. We give an e... more The concept of normal subalgebras in B- algebras is due to J. Neggers and H. S. Kim. We give an equivalent definition and show that the center Z(A )o f a B-algebra A is a normal subalgebra of A. Moreover, we prove that the notion of a normal subalgebra is equivalent to the normal subgroup of the derived group. Hence the lattices of normal subalgebras (and also the congruence lattices) of B-algebras are modular. 1 Preliminaries B-algebras have been introduced by J. Neggers and H. S. Kim in (4). They defined a B-algebra as an algebra (A; ∗,0) of type (2,0) (i.e., a nonempty set A with a binary operation ∗ and a constant 0) satisfying the following axioms:
Scientiae mathematicae Japonicae, 2015
Journal of Multiple-Valued Logic and Soft Computing, 2018
Demonstratio Mathematica
Andrzej Walendziak STRONGNESS IN LATTICES Dedicated to Professor Tadeusz Traczyk Faigle [3] intro... more Andrzej Walendziak STRONGNESS IN LATTICES Dedicated to Professor Tadeusz Traczyk Faigle [3] introduced the notion of a strong join-irreducible element in lattices of finite length. In this note we extend the concept of strongness to arbitrary lattices being not necessarily of finite length. Here we give a generalization of some results of papers [3] and [5].
In this paper, the concepts of branchwise commutative pseudo-CI algebras and pointed pseudo-CI al... more In this paper, the concepts of branchwise commutative pseudo-CI algebras and pointed pseudo-CI algebras are introduced and some of their properties are investigated
Portugaliae Mathematica, 1994
Any atomistic lattice is strong whereas the converse does not hold, in general. In the present pa... more Any atomistic lattice is strong whereas the converse does not hold, in general. In the present paper we prove that, if in a strong atomic J-lattice, each atom has a complement, then the lattice is atomistic. This result generalizes the theorem of [2].
In this paper we investigate the relationship between BE-algebras, implicative algebras, and J-al... more In this paper we investigate the relationship between BE-algebras, implicative algebras, and J-algebras. Moreover, we define commutative BE-algebras and state that these algebras are equivalent to the commutative dual BCK-algebras.
The concepts of semisimple, Archimedean, and semilocal pseudo MV -algebras are investigated and m... more The concepts of semisimple, Archimedean, and semilocal pseudo MV -algebras are investigated and many interesting facts concerning them are given.
J. Multiple Valued Log. Soft Comput., 2018
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Papers by Andrzej Walendziak