Structure of commutative cancellative integral residuated lattices on (0, 1]

• Autores: Rostislav Horcík
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 57, Nº. 3, 2007, págs. 303-332
• Idioma: inglés
• DOI: 10.1007/s00012-007-2050-0
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• Resumen

  • ?MTL-algebras were introduced as an algebraic counterpart of the cancellative extension of monoidal t-norm based logic. It was shown that they form a variety generated by ?MTL-chains on the real interval [0, 1]. In this paper the structure of these generators is investigated. The results illuminate the structure of cancellative integral commutative residuated chains, because every such algebra belongs to the quasivariety generated by the zero-free subreducts on (0, 1] of all ?MTL-chains on [0, 1].