# Article

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Keywords:
generalized $MV$-algebra; representability; congruence relation; unital lattice ordered group
Summary:
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.
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