Decomposability of the Finitely Generated Free Hoop Residuation Algebra

摘要

In this paper we prove that, for n > 1, the n-generated free algebra in any locally finite subvariety of HoRA can be written in a unique nontrivial way as L_2 × A′, where A′ is a directly indecomposable algebra inν . More precisely, we prove that the unique nontrivial pair of factor congruences of F_ν(n) is given by the filters and , F_v(n)(i]where the element is recursively defined from the term j(x,y)=(((x→y)→y)→x)→x introduced by W. H. Cornish. As an additional result we obtain a characterization of minimal irreducible filters of F_ν(n) in terms of its coatoms.