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

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    0348399 - UIVT-O 2011 RIV CH eng J - Článek v odborném periodiku
    Horčík, Rostislav
    Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers.
    Algebra Universalis. Roč. 63, 2-3 (2010), s. 261-274 ISSN 0002-5240
    Grant CEP: GA AV ČR KJB100300701
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: residuated lattice * cancellative commutative residuated lattice * subvariety lattice * submonoid of natural numbers
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.479, rok: 2010

    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.
    Trvalý link: http://hdl.handle.net/11104/0188946
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