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Keywords:
$DRl$-monoid; prime ideal; spectrum; $MV$-algebra
Summary:
Ordered prime spectra of Boolean products of bounded $DRl$-monoids are described by means of their decompositions to the prime spectra of the components.
References:
[1] S. Burris H. P. Sankappanavar: A Course in Universal Algebra. Springer-Verlag, Berlin, 1977. MR 0648287
[2] C. C. Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467-490. DOI 10.1090/S0002-9947-1958-0094302-9 | MR 0094302 | Zbl 0084.00704
[3] C. C. Chang: A new proof of the completeness of the Lukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959), 74-80. MR 0122718 | Zbl 0093.01104
[4] R. Cignoli A. Torrens: The poset of prime l-ideaІs of an abelian l-group with a strong unit. J. Algebra 184 (1996), 604-614. DOI 10.1006/jabr.1996.0278 | MR 1409232
[5] T. Kovář: A general theory of dually residuated lattice ordered monoids. Thesis, Palacký Univ. Olomouc, 1996.
[6] D. Mundici: Interpretation of AF C*-algebras jn Lukasiewicz sentential calculus. J. Funct. Analys. 65 (1986), 15-63. DOI 10.1016/0022-1236(86)90015-7 | MR 0819173
[7] J. Rachůnek: Spectra of autometrized lattice algebras. Math. Bohem. 123 (1998), 87-94. MR 1618727
[8] J. Rachůnek: DRl-semigroups and MV-algebras. Czechoslovak Math. J. 48 (1998), 365-372. DOI 10.1023/A:1022801907138 | MR 1624268
[9] J. Rachůnek: MV-algebras are categorically equivalent to a class of $DRl_{1(i)}$-semigroups. Math. Bohem. 123 (1998), 437-441. MR 1667115
[10] J. Rachůnek: Polars and annihilators in representable DRl-monoids and MV-algebras. (submitted).
[11] K. L. N. Swamy: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105-114. DOI 10.1007/BF01360284 | MR 0183797 | Zbl 0138.02104
[12] K. L. N. Swamy: Dually residuated lattice ordered semigroups II. Math. Ann. 160 (1965), 64-71. DOI 10.1007/BF01364335 | MR 0191851
[13] K. L. N.Swamy: Dually residuated lattice ordered semigroups III. Math. Ann. 167 (1966), 71-74. DOI 10.1007/BF01361218 | MR 0200364
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