Free Nilpotent Minimum Algebras.

BUSANICHE, MANUELA

Garnagno, Italia

Conferencia; International Conference on the Algebraic and Logical Foundations of Many-Valued Reasoning; 2006

Nilpotent minimum algebras (NM-algebras, for short) are bounded residuated lattices that satisfy three extra axioms: prelinearity, involution and the nilpotent minimum axiom, which roughly states that the conjunction of two elements is either their minimum or the bottom element in the lattice. We will give a description of the free algebra in the variety of NMalgebras as weak boolean product of directly indecomposable NMalgebras over the spectrum of its boolean skeleton. These directly indecomposable algebras turn out to be connected or disconnected rotations (see [1]) of free algebras in the variety of generalized G¨odel algebras (prelinear unbounded Heyting algebras). The boolean skeleton of the free algebra is a free boolean algebra over a poset. [1] S. Jenei, On the structure of rotation invariant semigroups. Arch. Math. Logic 42, 489-514 (2003).42, 489-514 (2003). 1