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2004 | 2 | 2 | 199-217
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Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

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The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.
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Czasopismo
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Tom
2
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2
Strony
199-217
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wydano
2004-04-01
online
2004-04-01
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Bibliografia
  • [1] D. Buşneag: “Hilbert algebra of fractions and maximal Hilbert algebras of quotients”, Kobe Journal of Mathematics, Vol. 5, (1988), pp. 161–172.
  • [2] D. Buşneag and D. Piciu: Meet-irreducible ideals in an MV-algebra, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXVIII, 2001, pp. 110–119.
  • [3] D. Buşneag and D. Piciu: “On the lattice of ideals of an MV-algebra”, Scientiae Mathematicae Japonicae, Vol. 56, No. 2, (2002), pp. 367–372, e6, pp. 221–226.
  • [4] D. Buşneag and D. Piciu: MV-algebra of fractions relative to an λ-closed system, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXX, 2003, pp. 1–6.
  • [5] D. Buşneag and D. Piciu: “MV-algebra of fractions and maximal MV-algebra of quotients”, to appear in Journal of Multiple-Valued Logic and Soft Computing.
  • [6] C.C. Chang: “Algebraic analysis of many valued logics”, Trans. Amer. Math. Soc., Vol. 88, (1958), pp. 467–490. http://dx.doi.org/10.2307/1993227
  • [7] R. Cignoli, I.M.L. D'Ottaviano and D. Mundici: Algebraic foundation of many-valued Reasoning, Kluwer Academic Publishers, Dordrecht, 2000.
  • [8] W.H. Cornish: “The multiplier extension of a distributive lattice”, Journal of Algebra, Vol. 32, (1974), pp. 339–355. http://dx.doi.org/10.1016/0021-8693(74)90143-4
  • [9] W.H. Cornish: “A multiplier approach to implicative BCK-algebras”, Mathematics Seminar Notes, Kobe University, Vol. 8, No. 1, (1980), pp. 157–169.
  • [10] C. Dan: F-multipliers and the localisation of Heyting algebras, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXIV, 1997, pp. 98–109.
  • [11] A. Dvurečenskij: “Pseudo-MV-algebras are intervals in l-groups”, Journal of Australian Mathematical Society, Vol. 72, (2002), pp. 427–445. http://dx.doi.org/10.1017/S1446788700036806
  • [12] G. Georgescu and A. Iorgulescu: “Pseudo-MV algebras”, Multi. Val. Logic, Vol. 6, (2001), pp. 95–135.
  • [13] P. Hájek: Metamathematics of fuzzy logic Kluwer Acad. Publ., Dordrecht, 1998.
  • [14] J. Lambek: Lectures on Rings and Modules, Blaisdell Publishing Company, 1966.
  • [15] I. Leuştean: “Local Pseudo-MV algebras”, Soft Computing, Vol. 5, (2001), pp. 386–395. http://dx.doi.org/10.1007/s005000100141
  • [16] D. Piciu: Pseudo-MV algebra of fractions relative to an λ-closed system, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXX, 2003, pp. 7–13.
  • [17] J. Schmid: “Multipliers on distributive lattices and rings of quotients”, Houston Journal of Mathematics, Vol. 6, No. 3, (1980), pp. 401–425.
  • [18] J. Schmid: Distributive lattices and rings of quotients, Coll. Math. Societatis Janos Bolyai, Szeged, Hungary, 1980.
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bwmeta1.element.doi-10_2478_BF02476540
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