On the direct decomposability of pseudo-t-norms, t-norms and implication operators on product lattices

In this paper, we discuss the direct decomposability of pseudo-t-norms and t-norms on a product lattice, characterize the implication operator on a product lattice that is a direct product of two implication operators and study the direct decomposability of S-implications, R-implications, n-reciprocal R-implications and n-reciprocal QL-implications on a product lattice.