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Archimedean Residuated LatticesDOI: 10.2478/v10157-010-0017-5 Keywords: residuated lattice, boolean algebra, archimedean, hyperarchimedean residuated lattice, deductive system, irreducible element, prime deductive system, maximal deductive system Abstract: For a residuated lattice A we denote by Ds(A) the lattice of all deductive systems (congruence filters) of A. The aim of this paper is to put in evidence new characterizations for maximal and prime elements of Ds(A) and to characterize archimedean and hyperarchimedean residuated lattices; so we prove some theorems of Nachbin type for residuated lattices. These results generalize to the case of residuated lattices some results earlier obtained by Bu neag and Piciu for the case of BL-algebras.
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