Banaschewski’s theorem for generalized M V -algebras

Ján Jakubík

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 4, page 1099-1105
  • ISSN: 0011-4642

Abstract

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A generalized M V -algebra 𝒜 is called representable if it is a subdirect product of linearly ordered generalized M V -algebras. Let S be the system of all congruence relations ρ on 𝒜 such that the quotient algebra 𝒜 / ρ is representable. In the present paper we prove that the system S has a least element.

How to cite

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Jakubík, Ján. "Banaschewski’s theorem for generalized $MV$-algebras." Czechoslovak Mathematical Journal 57.4 (2007): 1099-1105. <http://eudml.org/doc/31184>.

@article{Jakubík2007,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized $MV$-algebra; representability; congruence relation; unital lattice ordered group; generalized MV-algebra; representability; congruence relation; unital lattice-ordered group},
language = {eng},
number = {4},
pages = {1099-1105},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Banaschewski’s theorem for generalized $MV$-algebras},
url = {http://eudml.org/doc/31184},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Jakubík, Ján
TI - Banaschewski’s theorem for generalized $MV$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1099
EP - 1105
AB - 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.
LA - eng
KW - generalized $MV$-algebra; representability; congruence relation; unital lattice ordered group; generalized MV-algebra; representability; congruence relation; unital lattice-ordered group
UR - http://eudml.org/doc/31184
ER -

References

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