Geodesic
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 
@article{CMJ_2007_57_4_a2,
     author = {Jakub{\'\i}k, J\'an},
     title = {Banaschewski{\textquoteright}s theorem for generalized $MV$-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1099--1105},
     year = {2007},
     volume = {57},
     number = {4},
     mrnumber = {2357582},
     zbl = {1174.06318},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a2/}
}
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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/