State morphism MV-algebras
A. Dvurecenskij, T. Kowalski, F. Montagna
TL;DR
This paper characterizes subdirectly irreducible MV-algebras with internal states, classifies state morphism MV-algebras, and explores the variety of such algebras, revealing a continuum of subvarieties.
Contribution
It provides a complete classification of subdirectly irreducible SMMV-algebras and describes their generators, advancing the structural understanding of these algebraic systems.
Findings
Classification of subdirectly irreducible SMMV-algebras
Description of single generators of the variety
Existence of a continuum of varieties of SMMV-algebras
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.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge