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Communicated by A. Di Nola.
In the last decade, interest in projective MV-algebras has grown greatly; see Cabrer and Mundici (Algebra Univ 62(1):63–74, 2009), Di Nola et al. (Int J Approx Reason 47(3):323–332, 2008) and Di Nola and Grigolia (J Multiple-Valued Logic Soft Comput 9(3):291–317, 2003). In this paper, we establish a necessary and sufficient condition for \(n\) elements of the free \(n\)-generator MV-algebra to generate a projective MV-algebra. This generalizes the characterization of the \(n\) free generators proved in Lacava (Algebra Univ 57(4):455–462, 2007). Using this, some classes of projective generators for bigenerated MV-algebras, are given. In particular, some effective procedures to determine, by elementary methods, generators of projective MV-algebras are explained.
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Cabrer LM, Mundici D (2009) Projective MV-algebras and rational polyhedra. Algebra Univ 62(1):63–74
Cignoli R, D’Ottaviano I, Mundici D (2000) Algebraic foundations of many-valued reasoning. In: Trends in logic. Kluwer, Dordrecht
Di Nola A, Grigolia R (2003) Projective MV-algebras and their automorphism groups. J Multiple-Valued Logic Soft Comput 9(3):291–317
- Generators of projective MV-algebras
- Publication date
- Springer Berlin Heidelberg
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