On idempotent modifications of $MV$-algebras

Jakubík, Ján. "On idempotent modifications of $MV$-algebras." Czechoslovak Mathematical Journal 57.1 (2007): 243-252. <http://eudml.org/doc/31127>.

@article{Jakubík2007,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {$MV$-algebra; idempotent modification; subdirect reducibility; MV-algebra; idempotent modification; subdirect irreducibility},
language = {eng},
number = {1},
pages = {243-252},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On idempotent modifications of $MV$-algebras},
url = {http://eudml.org/doc/31127},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Jakubík, Ján
TI - On idempotent modifications of $MV$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 243
EP - 252
AB - 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.
LA - eng
KW - $MV$-algebra; idempotent modification; subdirect reducibility; MV-algebra; idempotent modification; subdirect irreducibility
UR - http://eudml.org/doc/31127
ER -