Czechoslovak Mathematical Journal, Vol. 58, No. 1, pp. 183-202, 2008

Direct summands and retract mappings of generalized $MV$-algebras

Jan Jakubik

Jan Jakubik, Mathematical Institute, Slovak Academy of Sciences, Gresakova 6, SK-040 01 Kosice, Slovakia, e-mail: kstefan@saske.sk

Abstract: 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.

Keywords: residuated lattice, lattice ordered group, generalized $MV$-algebra, direct summand

Classification (MSC 2000): 06D35, 06F15


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