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Keywords:
residuated lattice; lattice ordered group; generalized $MV$-algebra; direct summand
residuated lattice; lattice ordered group; generalized $MV$-algebra; direct summand
Summary:
In the present paper we deal with generalized $MV$-algebras ($GMV$-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, $GMV$-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of $GMV$-algebras. The relations between $GMV$-algebras and lattice ordered groups are essential for this investigation.
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