A non-commutative generalization of $MV$-algebras
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 255-273 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 06D35, 06F05, 06F15
@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/}
}
TY  - JOUR
AU  - Rachůnek, Jiří
TI  - A non-commutative generalization of $MV$-algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 255
EP  - 273
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a2/
LA  - en
ID  - CMJ_2002_52_2_a2
ER  - 
%0 Journal Article
%A Rachůnek, Jiří
%T A non-commutative generalization of $MV$-algebras
%J Czechoslovak Mathematical Journal
%D 2002
%P 255-273
%V 52
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a2/
%G en
%F 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