Isometries of generalized $MV$-algebras
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 161-171

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In this paper we investigate the relations between isometries and direct product decompositions of generalized $MV$-algebras.
In this paper we investigate the relations between isometries and direct product decompositions of generalized $MV$-algebras.
Classification : 03G25, 06D35
Keywords: generalized $MV$-algebra; isometry; direct product decomposition
Jakubík, Ján. Isometries of generalized $MV$-algebras. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 161-171. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a13/
@article{CMJ_2007_57_1_a13,
     author = {Jakub{\'\i}k, J\'an},
     title = {Isometries of generalized $MV$-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {161--171},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309957},
     zbl = {1174.06316},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a13/}
}
TY  - JOUR
AU  - Jakubík, Ján
TI  - Isometries of generalized $MV$-algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 161
EP  - 171
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a13/
LA  - en
ID  - CMJ_2007_57_1_a13
ER  - 
%0 Journal Article
%A Jakubík, Ján
%T Isometries of generalized $MV$-algebras
%J Czechoslovak Mathematical Journal
%D 2007
%P 161-171
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a13/
%G en
%F CMJ_2007_57_1_a13

[1] G. Birkhoff: Lattice Theory. American Mathematical Society, Providence, 1967. | MR | Zbl

[2] R. Cignoli, I. M. I. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-valued Reasoning. Kluwer Academic Publishers, Dordrecht, 2000. | MR

[3] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. | Zbl

[4] A. Dvurečenskij: Pseudo $MV$-algebras are intervals of $\ell $-groups. J. Austral. Math. Soc. 72 (2002), 427–445. | DOI | MR

[5] G. Georgescu and A. Iorgulescu: Pseudo $MV$-algebras: a non-commutative extension of $MV$-algebras. Proc. Fourth. Internal Symp. Econ. Inf., INFOREC, Bucharest, 1999, pp. 961–968.

[6] G. Georgescu and A. Iorgulescu: Pseudo $MV$-algebras. Multiple-Valued Logic 6 (2001), 95–135. | MR

[7] Ch. Holland: Intrinsic metrics for lattice ordered groups. Alg. Universalis 19 (1984), 142–150. | DOI | MR | Zbl

[8] J. Jakubík: Isometries of lattice ordered groups. Czechoslovak Math. J. 30 (1980), 142–152. | MR

[9] J. Jakubík: On intervals and isometries of $MV$-algebras. Czechoslovak Math. J. 52 (2002), 651–663. | DOI | MR

[10] J. Jakubík: Direct product decompositions of pseudo $MV$-algebras. Archivum math. 37 (2001), 131–142. | MR

[11] J. Jakubík: Isometries of $MV$-algebras. Math. Slovaca 54 (2004), 43–48. | MR

[12] J. Rachůnek: A non-commutative generalization of $MV$-algebras. Czechoslovak Math. J. 52 (2002), 255–273. | DOI | MR

[13] K. L. Swamy: Izometries in autometrized lattice ordered groups. Algebra Univ. 8 (1977), 58–64.