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On intervals and isometries of MV-algebras. (English) Zbl 1012.06013
Summary: 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.

MSC:
06D35 MV-algebras
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References:
[1] G. Birkhoff: Lattice Theory. AMS Colloquium Publications. Vol. XXV, Providence, RI, 1967. · Zbl 0153.02501
[2] G. Cattaneo and F. Lombardo: Independent axiomatization of \(MV\)-algebras. Tatra Mt. Math. Publ. 15 (1998), 227-232. · Zbl 0939.03076
[3] C. C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467-490. · Zbl 0084.00704
[4] P. Conrad: Lattice Ordered Groups. Tulane University, New Orleans, 1970. · Zbl 0258.06011
[5] D. Glushankof: Cyclic ordered groups and \(MV\)-algebras. Czechoslovak Math. J. 44(119) (1994), 725-739.
[6] Ch. Holland: Intrinsic metrics for lattice ordered groups. Algebra Universalis 19 (1984), 142-150. · Zbl 0557.06011
[7] J. Jakubík: Isometries of lattice ordered groups. Czechoslovak Math. J. 30(105) (1980), 142-152. · Zbl 0436.06013
[8] J. Jakubík: Direct product decompositions of \(MV\)-algebras. Czechoslovak Math. J. 44(119) (1994), 725-739. · Zbl 0821.06011
[9] J. Jakubík and M. Kolibiar: On some properties of pairs of lattices. Czechoslovak Math. J. 4(79) (1954), 1-27. · Zbl 0059.02601
[10] M. Jasem: Weak isometries and direct decompositions of dually residuated lattice ordered semigroups. Math. Slovaca 43 (1993), 119-136. · Zbl 0782.06012
[11] J. Lihová: Posets having a selfdual interval poset. Czechoslovak Math. J. 44(119) (1994), 523-533. · Zbl 0822.06001
[12] P. Mangani: On certain algebras related to many-valued logics. Boll. Un. Mat. Ital. 8 (1973), 68-78.
[13] D. Mundici: Interpretation of \(AFC^*\)-algebras in Łukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-63. · Zbl 0597.46059
[14] W. B. Powell: On isometries in abelian lattice ordered groups. J. Indian Math. Soc. 46 (1982), 189-194. · Zbl 0614.06012
[15] J. Rachůnek: Isometries in ordered groups. Czechoslovak Math. J. 34(109) (1984), 334-341. · Zbl 0558.06020
[16] K. L. Swamy: Isometries in autometrized lattice ordered groups. Algebra Universalis 8 (1977), 58-64. · Zbl 0457.06015
[17] K. L. Swamy: Isometries in autometrized lattice ordered groups II. Math. Seminar Notes, Kobe Univ. 5 (1977), 211-214. · Zbl 0457.06015
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