Infinitely ∨-distributive t-norms on complete lattices and pseudo-complements

In this paper, we have introduced the concepts of T-prime element. T-prime radical element and T-semi-prime element and have studied their properties. We have investigated the construction methods of new infinitely boolean OR-distributive t-norms from given infinitely v-distributive t-norms by means of T-prime elements and pseudo-conlplements. If every element of L is T-prime radical element. then we show that L is a complete Brouwerian lattice and T = boolean AND. If L is all algebraic lattice, T is a t-norm oil L and every compact element of L is idempotent, then we obtain that T = boolean AND. We show that L(R) is a complete lattice and that the restriction of T to L(R) is an infinitely boolean OR-distributive t-norm on L(R). When T is an infinitely boolean OR-distributive t-norm on L and 0 is a T-prime, we present infinitely boolean OR-distributive t-norms on a complete sublattice L* and study their properties. (C) 2008 Elsevier B.V. All rights reserved.