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Banaschewski’s theorem for generalized $MV$-algebras
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1099-1105 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A generalized $MV$-algebra $\mathcal A$ is called representable if it is a subdirect product of linearly ordered generalized $MV$-algebras. Let $S$ be the system of all congruence relations $\rho $ on $\mathcal A$ such that the quotient algebra $\mathcal A/\rho $ is representable. In the present paper we prove that the system $S$ has a least element.
A generalized $MV$-algebra $\mathcal A$ is called representable if it is a subdirect product of linearly ordered generalized $MV$-algebras. Let $S$ be the system of all congruence relations $\rho $ on $\mathcal A$ such that the quotient algebra $\mathcal A/\rho $ is representable. In the present paper we prove that the system $S$ has a least element.
Classification : 06D35, 06F15
Keywords: generalized $MV$-algebra; representability; congruence relation; unital lattice ordered group 
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     title = {Banaschewski{\textquoteright}s theorem for generalized $MV$-algebras},
     journal = {Czechoslovak Mathematical Journal},
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Jakubík, Ján. Banaschewski’s theorem for generalized $MV$-algebras. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1099-1105. http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a2/

[1] B. Banaschewski: On lattice-ordered groups. Fund. Math. 55 (1964), 113–122. | DOI | MR | Zbl

[2] G. Birkhoff: Lattice Theory. Third Edition, Providence, 1967. | MR | Zbl

[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] A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht, 2000. | MR

[6] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras. In: The Proceedings of the Fourth International Symposium on Economic Informatics, INFOREC, Bucharest, 6–9 May, Romania, 1999, pp. 961–968. | MR

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

[8] J. Jakubík: Normal prime filters of a lattice ordered group. Czech. Math. J. 24 (1974), 91–96. | MR

[9] J. Jakubík: Subdirect product decompositions of MV-algebras. Czech. Math. J. 49 (1999), 163–173. | DOI | MR

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