
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.
Varietie, MV-algebra, MV-algebra; State MV-algebra; State morphism MV-algebra; Varieties; Subdirectly irreducible algebra; Cover variety, Commutative Algebra (math.AC), state morphism MV-algebra, 510, Theoretical Computer Science, Artificial Intelligence, state MV-algebra, FOS: Mathematics, 06D35, Subdirectly irreducible algebra, MV-algebras, Applied Mathematics, Varieties, Cover variety, cover variety, State morphism MV-algebra, subdirectly irreducible algebra, Mathematics - Commutative Algebra, State MV-algebra, Many-valued logic, 03B50, Software
Varietie, MV-algebra, MV-algebra; State MV-algebra; State morphism MV-algebra; Varieties; Subdirectly irreducible algebra; Cover variety, Commutative Algebra (math.AC), state morphism MV-algebra, 510, Theoretical Computer Science, Artificial Intelligence, state MV-algebra, FOS: Mathematics, 06D35, Subdirectly irreducible algebra, MV-algebras, Applied Mathematics, Varieties, Cover variety, cover variety, State morphism MV-algebra, subdirectly irreducible algebra, Mathematics - Commutative Algebra, State MV-algebra, Many-valued logic, 03B50, Software
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