State morphism MV-algebras

Authors:
Anatolij DvurečEnskij;Tomasz Kowalski;Franco Montagna
Affiliations:
Mathematical Institute, Slovak Academy of Sciences Štefánikova 49, SK-814 73 Bratislava, Slovakia;Department of Mathematics and Statistics, University of Melbourne Parkville, VIC 3010, Australia;Università Degli Studi di Siena, Dipartimento di Scienze Matematiche e Informatiche “Roberto Magari”, Pian dei Mantellini 44, I-53100 Siena, Italy
Venue:
International Journal of Approximate Reasoning
Year:
2011

Citing 5
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Abstract

We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators of the variety of SMMV-algebras, and show that we have a continuum of varieties of SMMV-algebras.