1. Covers of the Abelian Variety of Generalized MV-Algebras.
- Author
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Dvurečenskij, Anatolij and Holland, W. Charles
- Subjects
- *
ABELIAN varieties , *ALGEBRAIC geometry , *MATHEMATICAL continuum , *MATHEMATICAL analysis , *ALGEBRA - Abstract
Using the categorical equivalence of the class of generalized MV-algebras with the class of unital ℓ-groups, we describe all varieties of symmetric top abelian unital ℓ-groups that cover the variety Auℓ of abelian unital ℓ-groups. Equivalently, we describe all cover varieties of the variety of MV-algebras, MV, within the variety of generalized MV-algebras admitting only one negation and each of whose maximal ideals is normal. In particular, there are continuum many representable varieties of generalized MV-algebras that cover MV. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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