It is an old open question whether a t-norm with a continuous
diagonal must be continuous [7]. We give a partial positive answer for t-norms
with noncontinuous additive generators (constructed by the technique of [1, 3]).
Besides this, we give necessary and sufficient conditions for a function to be
the diagonal of a continuous t-norm, and we characterize all continuous t-norms
with a given diagonal (according to [6]).
