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Title: On ideals in De Morgan residuated lattices (English)
Author: Holdon, Liviu-Constantin
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 54
Issue: 3
Year: 2018
Pages: 443-475
Summary lang: English
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Category: math
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Summary: In this paper, we introduce a new class of residuated lattices called De Morgan residuated lattices, we show that the variety of De Morgan residuated lattices includes important subvarieties of residuated lattices such as Boolean algebras, MV-algebras, BL-algebras, Stonean residuated lattices, MTL-algebras and involution residuated lattices. We investigate specific properties of ideals in De Morgan residuated lattices, we state the prime ideal theorem and the pseudo-complementedness of the ideal lattice, we pay attention to prime, maximal, $\odot$-prime ideals and to ideals that are meet-irreducible or meet-prime in the lattice of all ideals. We introduce the concept of an annihilator of a given subset of a De Morgan residuated lattice and we prove that annihilators are a particular kind of ideals. Also, regular annihilator and relative annihilator ideals are considered. (English)
Keyword: residuated lattice
Keyword: De Morgan laws
Keyword: filter
Keyword: deductive system
Keyword: ideal
Keyword: $\cap $-prime
Keyword: $\cap $-irreducible
Keyword: annihilator
MSC: 03B22
MSC: 03G05
MSC: 03G25
MSC: 06A06
MSC: 08A72
DOI: 10.14736/kyb-2018-3-0443
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Date available: 2018-11-02T10:06:55Z
Last updated: 2018-11-02
Stable URL: http://hdl.handle.net/10338.dmlcz/147431
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