Abstract
In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.
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References
R. Ambrosio andA. Lettieri,A Classification of Bipartite MV-algebras Math. Japon 38 1, 1993, pp. 111–117.
M. Anderson andT. Feil,Lattice-Ordered Groups: an Introduction D. Reidel Publ. Co., Dordrecht, Kluwer Academic Publishers, Dordrecht/Boston/London 1987.
L. P. Belluce,Semisimple Algebras of Infinite-valued Logic Canadian J. Math. 38 1986, pp. 1356–1379.
L. P. Belluce, A. Di Nola andA. Lettieri,Local MV-Algebras, Rendiconti del Circolo Matematico di Palermo, Vol. 42 1993.
M. W. Beynon,Duality Theorems for Finitely Generated Vector Lattices, Proc. London Math. Soc. (3) 31, 1995
M. W. Beynon,Applications of Duality in the Theory of Finitely Generated Lattice-ordered Abelian Groups Canadian J. Math. 2 1997, pp. 243–254.
G. Birkhoff,Lattice Theory, 3nd edition, Amer. Math. Soc. Coll. Publ. 25, New York 1979.
S. Burris andH. Sankappanavar,A Course in Universal Algebra, Graduate Texts in Mathematics 78 Springer-Verlag, New York-Heidelberg-Berlin 1981.
C. C. Chang,Algebraic Analysis of Many Valued Logics Trans. Amer. Math. Soc. 88 1958, pp. 467–490.
C.C. Chang,A New Proof of the Completeness of the Lukasiewicz axioms Trans. Amer. Math. Soc. 93 1959, pp. 74–80.
W. H. Cornish,Lattice-ordered Groups and BCK-algebras Math. Japon. 25 4, 1980, pp. 471–476.
A. Di Nola, F. Liguori andS. Sessa,Using Maximal Ideals in the Classification of MV-algebras, Portugaliae Math. Vol. 50 Fasc. 1, 1993, pp. 87–102.
L. Fuchs,Partially Ordered Algebraic Systems Pergamon Press, Oxford 1963.
C. S. Hoo,MV-algebras, Ideals and Simplicity Math. Japon. 34 4, 1989, pp. 563–583.
W. Komori,Super-Lukasiewicz Propositional Logics Nagoya Math. J. Vol. 84, 1981, pp. 119–133.
S. MacLane,Categories for the Working Mathematician Springer-Verlag, New York 1979.
D. Mundici,Interpretation of AF C*-algebras in Lukasiewicz sentential calculus J. Funct. Anal.,65 1986, pp. 15–63.
D. Mundici,Free Products in the Category of Abelian l-groups with Strong Unit J. of Algebra Vol. 113, 1, 1988, pp. 89–109.
E. C. Weinberg,Free Lattice Ordered Abelian Groups Math Ann.,151 1963, pp. 187–199.
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Di Nola, A., Lettieri, A. Perfect MV-algebras are categorically equivalent to abelianl-groups. Stud Logica 53, 417–432 (1994). https://doi.org/10.1007/BF01057937
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DOI: https://doi.org/10.1007/BF01057937