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Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers

SYSNO ASEP	0348399
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers
Author(s)	Horčík, Rostislav (UIVT-O)_{SAI, RID}
Source Title	Algebra Universalis. - : Springer - ISSN 0002-5240 Roč. 63, 2-3 (2010), s. 261-274
Number of pages	14 s.
Language	eng - English
Country	CH - Switzerland
Keywords	residuated lattice ; cancellative commutative residuated lattice ; subvariety lattice ; submonoid of natural numbers
Subject RIV	BA - General Mathematics
R&D Projects	KJB100300701 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000283085400010
EID SCOPUS	77958463567
DOI	10.1007/s00012-010-0076-1
Annotation	It is known that there are only two cancellative atoms in the subvariety lattice of residuated lattices, namely the variety of Abelian l-groups generated by the additive l-group of integers and the variety V generated by the negative cone of this l-group. In this paper we consider all cancellative residuated chains arising on 2-generated submonoids of natural numbers and show that almost all of them generate a cover of V. This proves that there are infinitely many covers above V which are commutative, integral, and representable.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2011

Number of the records: 1