Quotient Structures of Non-Commutative Residuated Lattices
Michiro Kondo · 2015
In this paper we consider some properties of noncommutative residuated lattices which are considered as an algebraic semantics of substructural logic. We show that there are always prime filters in a non-commutative residuated lattice X and that the intersection of the class Spec(X) of all prime filters of X is identical with {1}, that is, ∩ Spec(X) = {1}.