@article{CMJ_2002_52_2_a2,
author = {Rach\r{u}nek, Ji\v{r}{\'\i}},
title = {A non-commutative generalization of $MV$-algebras},
journal = {Czechoslovak Mathematical Journal},
pages = {255--273},
year = {2002},
volume = {52},
number = {2},
mrnumber = {1905434},
zbl = {1012.06012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a2/}
}
Rachůnek, Jiří. A non-commutative generalization of $MV$-algebras. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 255-273. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a2/
[1] V. D. Belousov: Foundations of the Theory of Quasigroups and Loops. Nauka, Moscow, 1967. (Russian) | MR
[2] A. Bigard, K. Keimel and S. Wolfenstein: Groupes et Anneaux Réticulés. SpringerVerlag, Berlin-Heidelberg-New York, 1977. | MR
[3] S. Burris and H. P. Sankappanavar: A Course in Universal Algebra. Springer-Verlag, Berlin-Heidelberg-New York, 1981. | MR
[4] C. C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467–490. | DOI | MR | Zbl
[5] C. C. Chang: A new proof of the completeness of the Lukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959), 74–80. | MR | Zbl
[6] R. Cignoli: Free lattice-ordered abelian groups and varieties of $MV$-algebras. Proc. IX. Latin. Amer. Symp. Math. Log., Part 1, Not. Log. Mat. 38 (1993), 113–118. | MR | Zbl
[7] Lattice-Ordered Groups (Advances and Techniques). A. M. W. Glass and W. Charles Holland (eds.), Kluwer Acad. Publ., Dordrecht-Boston-London, 1989. | MR | Zbl
[8] C. S. Hoo: $MV$-algebras, ideals and semisimplicity. Math. Japon. 34 (1989), 563–583. | MR | Zbl
[9] V. M. Kopytov and N. Ya. Medvedev: The Theory of Lattice Ordered Groups. Kluwer Acad. Publ., Dordrecht-Boston-London, 1994. | MR
[10] T. Kovář: A general theory of dually residuated lattice ordered monoids. Thesis, Palacký University Olomouc, 1996.
[11] D. Mundici: Interpretation of $AF C^{*}$-algebras in Łukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15–63. | MR | Zbl
[12] D. Mundici: $MV$-algebras are categorically equivalent to bounded commutative $BCK$-algebras. Math. Japon. 31 (1986), 889–894. | MR | Zbl
[13] J. Rachůnek: $DRl$-semigroups and $MV$-algebras. Czechoslovak Math. J. 48(123) (1998), 365–372. | DOI | MR
[14] J. Rachůnek: $MV$-algebras are categorically equivalent to a class of $DRl_{1(i)}$-semigroups. Math. Bohem. 123 (1998), 437–441. | MR
[15] K. L. N. Swamy: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105–114. | MR | Zbl
[16] K. L. N. Swamy: Dually residuated lattice ordered semigroups II. Math. Ann. 160 (1965), 64–71. | DOI | MR
[17] K. L. N. Swamy: Dually residuated lattice ordered semigroups III. Math. Ann. 167 (1966), 71–74. | DOI | MR | Zbl