In the framework of algebras with infinitary operations, an equational base for the category of σ-complete MV -algebras is given. In this way, we study some particular objects as simple algebras, directly irreducible algebras, injectives, etc. A completeness theorem respect to the standard MV -algebra, considered as σ-complete MV -algebra, is obtained. Finally we apply this result to the study of σ-complete Boolean algebras and σ-complete product MV -algebras.
Equational type characterization for sigma complete MV-algebras
FREYTES, HECTOR CARLOS
2013-01-01
Abstract
In the framework of algebras with infinitary operations, an equational base for the category of σ-complete MV -algebras is given. In this way, we study some particular objects as simple algebras, directly irreducible algebras, injectives, etc. A completeness theorem respect to the standard MV -algebra, considered as σ-complete MV -algebra, is obtained. Finally we apply this result to the study of σ-complete Boolean algebras and σ-complete product MV -algebras.
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