The t-Norms on a Bounded Posets

Abstract

In this presented note, t-norms (triangular norms) are studied in the general setting of bounded partially ordered sets(posets). The sets of idempotent elements, zero divisors and nilpotent elements associated to a t-norm are introduced and related to each other. The Archimedean property of t-norms is discussed, in particular its relationship to the diagonal inequality.