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On interval subalgebras of generalized MV-algebras. (English) Zbl 1141.06006
Every interval $$[a,b]$$ of a GMV-algebra $$A$$ is a GMV-algebra whose operations are defined as polynomials of $$A$$ (see [I. Chajda and J. Kühr, “GMV-algebras and meet-semilattices with sectionally antitone permutations”, Math. Slovaca 56, 275–288 (2006; Zbl 1141.06002)]). The present paper gives an alternative proof using the representation of $$A$$ via the functor $$\Gamma$$. Specifically, if $$A=\Gamma (G,u)$$ for a unital $$\ell$$-group $$(G,u)$$, then every interval $$[a,b]$$ of $$A$$ is equipped with operations inherited from $$G$$ making $$[a,b]$$ into a GMV-algebra. It is also shown that $$[a,b]$$ is always isomorphic to an interval subalgebra of the form $$[0,c]$$.

##### MSC:
 06D35 MV-algebras
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##### References:
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