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pseudo $MV$-algebras; lattice ordered group; unital lattice ordered group; variety
In this paper we investigate the relation between the lattice of varieties of pseudo $MV$-algebras and the lattice of varieties of lattice ordered groups.
[1] R.  Cignoli, M. I.  D’Ottaviano and D.  Mundici: Algebraic Foundations of many-valued Reasoning. Trends in Logic, Studia Logica Library, Vol.  7, Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097
[2] A.  Dvurečenskij: Pseudo $MV$-algebras are intervals in $\ell $-groups. J.  Austral. Math. Soc. (Ser.  A) 72 (2002), 427–445. DOI 10.1017/S1446788700036806 | MR 1902211
[3] A.  Dvurečenskij: States on pseudo $MV$-algebras. Studia Logica (to appear). MR 1865858
[4] G.  Georgescu and A.  Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras. In: The Proceedings of the Fourth International Symposium on Economic Informatics, Buchurest, Romania, 1999, pp. 961–968. MR 1730100
[5] G.  Georgescu and A.  Iorgulescu: Pseudo $MV$-algebras. Multiple-Valued Logic (a special issue dedicated to Gr. C.  Moisil) 6 (2001), 95–135. MR 1817439
[6] J.  Jakubík: Subdirect product decompositions of $MV$-algebras. Czechoslovak Math.  J. 49 (1999), 163–173. DOI 10.1023/A:1022472528113 | MR 1676813
[7] J.  Jakubík: Direct product decompositions of pseudo $MV$-algebras. Arch. Math. 37 (2001), 131–142. MR 1838410
[8] J. Rachůnek: A non-commutative generalization of $MV$-algebras. Czechoslovak Math. J. 52 (2002), 255–273. DOI 10.1023/A:1021766309509 | MR 1905434
[9] J.  Rachůnek: Prime spectra of non-commutative generalizations of $MV$-algebras. (Submitted).
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