Jan Jakubik, Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail: kstefan@saske.sk
Abstract: A generalized $MV$-algebra $\Cal A$ 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 $\Cal A$ such that the quotient algebra $\Cal A/\rho$ is representable. In the present paper we prove that the system $S$ has a least element.
Keywords: generalized $MV$-algebra, representability, congruence relation, unital lattice ordered group
Classification (MSC 2000): 06D35, 06F15
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