ArticleOriginal scientific text
Title
Congruences on semilattices with section antitone involutions
Authors 1
Affiliations
- Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic
Abstract
We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
Keywords
semilattice, section, antitone involution, congruence kernel, filter, congruence distributivity, 3-permutability
Bibliography
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Pages:
207-215
Main language of publication
English
Received
2009-12-14
Accepted
2010-04-21
Published
2010
DOI: 10.7151/dmgaa.1170
Exact and natural sciences