Geodesic
On idempotent modifications of $MV$-algebras
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 243-252 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an $MV$-algebra $\mathcal A$ we denote by $\mathcal A^{\prime }, A$ and $\ell (\mathcal A)$ the idempotent modification, the underlying set or the underlying lattice of $\mathcal A$, respectively. In the present paper we prove that if $\mathcal A$ is semisimple and $\ell (\mathcal A)$ is a chain, then $\mathcal A^{\prime }$ is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.
The notion of idempotent modification of an algebra was introduced by Ježek. He proved that the idempotent modification of a group is subdirectly irreducible. For an $MV$-algebra $\mathcal A$ we denote by $\mathcal A^{\prime }, A$ and $\ell (\mathcal A)$ the idempotent modification, the underlying set or the underlying lattice of $\mathcal A$, respectively. In the present paper we prove that if $\mathcal A$ is semisimple and $\ell (\mathcal A)$ is a chain, then $\mathcal A^{\prime }$ is subdirectly irreducible. We deal also with a question of Ježek concerning varieties of algebras.
Classification : 03G25, 06D35
Keywords: $MV$-algebra; idempotent modification; subdirect reducibility 
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     author = {Jakub{\'\i}k, J\'an},
     title = {On idempotent modifications of $MV$-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {243--252},
     year = {2007},
     volume = {57},
     number = {1},
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     zbl = {1174.06317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a19/}
}
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Jakubík, Ján. On idempotent modifications of $MV$-algebras. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 243-252. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a19/