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Prime spectra of non-commutative generalizations of MV-algebras. (English) Zbl 1058.06015
A GMV-algebra is a non-commutative generalization of an MV-algebra, introduced by the author and G. Georgescu and A. Iorgulescu. It is shown that GMV-algebras are special cases of Grishin algebras, which play an important role for classical bilinear logic. GMV-algebras correspond to a non-commutative logic between Łukasiewicz logic and the mentioned bilinear logic. The main purpose of the paper is to describe the properties of prime ideal spectra of GMV-algebras, their factor algebras and ideals and to prove that the spectrum of closed ideals of any GMV-algebra is homeomorphic to that of a completely distributive GMV-algebra.

MSC:
06D35 MV-algebras
03G25 Other algebras related to logic
06F15 Ordered groups
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