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Direct product factors in GMV-algebras. (English) Zbl 1113.06009
GMV-algebras (also known as pseudo-MV algebras) generalize MV-algebras, the algebras corresponding to Łukasiewicz logic, in that the addition is no longer assumed to be commutative. They are representable by intervals of \(\ell \)-groups.
In this paper, the internal direct product decompositions of a GMV-algebra are described, that is, the direct product decompositions such that each factor is among its ideals. The decompositions of a GMV-algebra are moreover related to those of the representing \(\ell \)-group.
Furthermore, the notion of projectibility is introduced for GMV-algebras in analogy to \(\ell \)-groups, and the polars of projectible GMV-algebras are characterized.
06D35 MV-algebras
06F15 Ordered groups
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