Simple Characterizations of Perfect Residuated Lattices
Michiro Kondo · 2016
We consider properties of local and of perfect residuated lattices in terms of filters and give characterization theorems of these residuated lattices. Moreover, we show that, for a perfect residuated lattice X, a set D(X) of elements with infinite order is a normal, maximal and Boolean filter. This implies that the quotient algebra X/D(X) is the two element Boolean algebra {0,1}.