Free nilpotent minumim algebras

BUSANICHE, MANUELA

MATHEMATICAL LOGIC QUARTERLY

Wiley-VCH

Año: 2006 vol. 52 p. 219 - 236

0942-5616

NM-algebras are the algebraic counterpart of  Nilpotent Minimum logic. This logic is a logic whose conjunction is interpreted by a left continuous (but not continuous) t-norm on the real segment [0,1] and the implication is interpreted by the adjoint of the t-norm. In the present paper we give a description of the free algebra over an arbitrary set of generators in the variety of nilpotent minimum algebras. Such description is given in terms of a weak Boolean product of directly indecomposable algebras over the Boolean space corresponding to the Boolean subalgebra of the free NM-algebra.