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Title: Implication and equivalential reducts of basic algebras (English)
Author: Chajda, Ivan
Author: Kolařík, Miroslav
Author: Švrček, Filip
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 49
Issue: 2
Year: 2010
Pages: 21-36
Summary lang: English
Category: math
Summary: A term operation implication is introduced in a given basic algebra $\mathcal {A}$ and properties of the implication reduct of $\mathcal {A}$ are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of $\mathcal {A}$ and, if this partial order is linear, the algebra $\mathcal {A}$ can be reconstructed by means of its equivalential reduct. (English)
Keyword: Basic algebra
Keyword: implication algebra
Keyword: implication reduct
Keyword: equivalential algebra
Keyword: equivalential reduct
MSC: 03G25
MSC: 06C15
MSC: 06D35
MSC: 08A62
idZBL: Zbl 1235.06010
idMR: MR2796944
Date available: 2011-02-18T07:34:34Z
Last updated: 2013-09-18
Stable URL:
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