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1
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.
2
Content available remote On implicative and maximal ideals of BL-algebras
Walendziak A.
Commentationes Mathematicae
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2014
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Vol 54, No. 2
247--258
EN
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 the homomorphic properties of implicative and maximal ideals.
3
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.
4
Content available remote On normal niters and congruence relations in BE-algebras
Walendziak A.
Commentationes Mathematicae
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2012
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Vol. 52, [Z] 2
199--205
EN
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 niters in A). Moreover, we give the construction of quotient algebra A/F of A via a normal filter F of A.
5
Content available remote Some characterizations of pseudo-BL-chains
Walendziak A., Wojciechowska-Rysiawa M.
Commentationes Mathematicae
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2011
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Vol. 51, [Z] 2
121-124
EN
Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.
6
Content available remote Bipartite pseudo-BL algebras
Walendziak A., Wojciechowska-Rysiawa M.
Demonstratio Mathematica
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2010
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Vol. 43, nr 3
487-496
EN
The class of bipartite pseudo-BL algebras (denoted by BP) and the class of strongly bipartite pseudo-BL algebras (denoted by BP0) are investigated. We prove that the class BP0 is a variety and show that BP is closed under subalgebras and arbitrary direct products but it is not a variety. We also study connections between bipartite pseudo-BL algebras and other classes of pseudo-BL algebras.
7
Content available remote Semisimple and semilocal pseudo BL-algebras
Walendziak A., Wojciechowska M.
Demonstratio Mathematica
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2009
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Vol. 42, nr 3
453-466
EN
The concepts of semisimple and semilocal pseudo BL-algebras are investigated. Many facts corresponding with them are considerated. Moreover, we give a negative answer to the question from [Di Nola, Georgescu and lorgulescu (Multiplae Valued Logic 8: 715-750, 2002), Problem 1.33].
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
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