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Start Over Creator Švrček, Filip

1. Interior and closure operators on bounded residuated lattice ordered monoids

Creator:
Švrček, Filip
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$GMV$-algebra, $DRl$-monoid, and filter
Language:
English
Description:
$GMV$-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior $GMV$-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on $DRl$-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on $GMV$-algebras.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Multiplicatively idempotent semirings

Creator:
Chajda, Ivan, Länger, Helmut, and Švrček, Filip
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
semiring, commutative semiring, multiplicatively idempotent semiring, semiring of characteristic 2, simple semiring, unitary Boolean ring, and bounded distributive lattice
Language:
English
Description:
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices. We get a characterization of this join.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Properties of relatively pseudocomplemented directoids

Creator:
Chajda, Ivan, Kolařík, Miroslav, and Švrček, Filip
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
directoid, relatively pseudocomplemented directoid, congruence distributivity, 3-permutability, residuated structure, adjointness property, and variety
Language:
English
Description:
The concept of a relatively pseudocomplemented directoid was introduced recently by the first author. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for relatively pseudocomplemented directoids. Hence, they can also be considered as residuated structures in a rather modified version. We also get two important congruence properties, namely congruence distributivity and 3-permutability valid in the variety V of relatively pseudocomplemented directoids. Then we show some basic results connected with subdirect irreducibility in V. Finally, we show another way how to introduce pseudocomplementation on directoids via relative pseudocomplementation.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public