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  1.  44
    Free Algebras in Varieties of Glivenko MTL-Algebras Satisfying the Equation 2(X2) = (2x)2.Roberto Cignoli & Antoni Torrens Torrell - 2006 - Studia Logica 83 (1-3):157-181.
    The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples to show how we can (...)
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  2.  22
    Free Algebras in Varieties of Glivenko MTL-Algebras Satisfying the Equation 2(X²) = (2x)².Roberto Cignoli & Antoni Torrens Torrell - 2006 - Studia Logica 83 (1-3):157 - 181.
    The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples to show how we can (...)
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  3. Bounded BCK-Algebras and Their Generated Variety.J. D. Gispert & Antoni Torrens Torrell - 2007 - Mathematical Logic Quarterly 53 (2):206-213.
    In this paper we prove that the equational class generated by bounded BCK-algebras is the variety generated by the class of finite simple bounded BCK-algebras. To obtain these results we prove that every simple algebra in the equational class generated by bounded BCK-algebras is also a relatively simple bounded BCK-algebra. Moreover, we show that every simple bounded BCK-algebra can be embedded into a simple integral commutative bounded residuated lattice. We extend our main results to some richer subreducts of the class (...)
     
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  4.  10
    Decomposability of Free Łukasiewicz Implication Algebras.Jose Patricio Díaz Varela & Antoni Torrens Torrell - 2006 - Archive for Mathematical Logic 45 (8):1011-1020.
    Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be (...)
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  5.  8
    Quasivarieties Generated by Simple MV-Algebras.Joan Gispert Brasó & Antoni Torrens Torrell - 1998 - Studia Logica 61 (1):79-99.
    In this paper we show that the quasivariety generated by an infinite simple MV-algebra only depends on the rationals which it contains. We extend this property to arbitrary families of simple MV-algebras.
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