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Using maximal ideals in the classification of MV-algebras. (English) Zbl 0799.06021
Summary: Since Chang’s pioneering algebraization of the infinite-valued sentential calculus of Łukasiewicz, ideal theory has proved a powerful unifying tool in the classification of MV-algebras and their categorical equivalents. In this paper, we investigate MV-algebras which are generated by some maximal ideal and MV-algebras where the maximal ideals form a closed subspace of the space of prime ideals. We describe the relationships of these classes to such classes as hyperarchimedean, local, perfect, semisimple and real MV-algebras. We also describe some properties of annihilator ideals.

MSC:
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
03G10 Logical aspects of lattices and related structures
03B50 Many-valued logic
54B35 Spectra in general topology
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