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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 \([0,c]\).

06D35 MV-algebras
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