A family of strict and discontinuous triangular norms

Answers to some questions about triangular norms are given. Precisely, a procedure of construction of infinitely many triangular norms is obtained (one for each operation ∗ : N2 → N such that 〈N <, ∗〉 is a strictly ordered commutative semigroup). Each of them is discontinuous at each point of a dense subset of [0, 1]2 and it satisfies the condition T(kx, y) = T(x,ky) for infinitely many k ϵ [0, 1].