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Algebra universalis

, Volume 69, Issue 2, pp 139–166 | Cite as

Equational type characterization for σ-complete MV-algebras

  • Hector Freytes
Article

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 with 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.

2010 Mathematics Subject Classification

Primary 06D35 Secondary 08A65 

Keywords and phrases

σ-complete MV-algebras infinitary operations Loomis–Sikorski Theorem 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Departamento de MatemáticaUNR-CONICETRosarioArgentina

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