مشخصات پژوهش

If S is a monoid, the set S × S equipped with componentwise S-action is called the diagonal act of S and is denoted by D(S). This gives an answer to a conjecture posed by Bulman-Fleming and Gilmour (Semigroup Forum 79:298–314, 2009). Besides, we present a fair characterization of monoids S over which the diagonal act D(S) is (principally) weakly flat and finally, we impose a condition on D(S) in order to make S a left PSF monoid.