Abstract
Let Int \(\mathcal{A}\) be the lattice of all intervals of an MV-algebra \(\mathcal{A}\). In the present paper we investigate the relations between direct product decompositions of \(\mathcal{A}\) and (i) the lattice Int \(\mathcal{A}\), or (ii) 2-periodic isometries on \(\mathcal{A}\), respectively.
Similar content being viewed by others
References
G. Birkhoff: Lattice Theory. AMS Colloquium Publications. Vol. XXV, Providence, RI, 1967.
G. Cattaneo and F. Lombardo: Independent axiomatization of MV –algebras. Tatra Mt. Math. Publ. 15 (1998), 227–232.
C. C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467–490.
P. Conrad: Lattice Ordered Groups. Tulane University, New Orleans, 1970.
D. Glushankof: Cyclic ordered groups and MV –algebras. Czechoslovak Math. J. 44(119) (1994), 725–739.
Ch. Holland: Intrinsic metrics for lattice ordered groups. Algebra Universalis 19 (1984), 142–150.
J. Jakubík: Isometries of lattice ordered groups. Czechoslovak Math. J. 30(105) (1980), 142–152.
J. Jakubík: Direct product decompositions of MV –algebras. Czechoslovak Math. J. 44(119) (1994), 725–739.
J. Jakubík and M. Kolibiar: On some properties of pairs of lattices. Czechoslovak Math. J. 4(79) (1954), 1–27. (In Russian.)
M. Jasem: Weak isometries and direct decompositions of dually residuated lattice ordered semigroups. Math. Slovaca 43 (1993), 119–136.
J. Lihová: Posets having a selfdual interval poset. Czechoslovak Math. J. 44(119) (1994), 523–533.
P. Mangani: On certain algebras related to many-valued logics. Boll. Un. Mat. Ital. 8 (1973), 68–78. (In Italian.)
D. Mundici: Interpretation of AFC*-algebras in Łukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15–63.
W. B. Powell: On isometries in abelian lattice ordered groups. J. Indian Math. Soc. 46 (1982), 189–194.
J. Rachůnek: Isometries in ordered groups. Czechoslovak Math. J. 34(109) (1984), 334–341.
K. L. Swamy: Isometries in autometrized lattice ordered groups. Algebra Universalis 8 (1977), 58–64.
K. L. Swamy: Isometries in autometrized lattice ordered groups II. Math. Seminar Notes, Kobe Univ. 5 (1977), 211–214.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jakubík, J. On intervals and isometries of MV-algebras. Czechoslovak Mathematical Journal 52, 651–663 (2002). https://doi.org/10.1023/A:1021792116546
Issue Date:
DOI: https://doi.org/10.1023/A:1021792116546