The Flatness Of The Diagonal Acts Of S

Let S be a monoid, D(S) be a diagonal acts of S.This thesis mainly investigate weakly pullback flatness, condition (PWPI), condi-tion (PI), condition (EI), weakly kernel flatness and condition (WPI), and give the characterization of monoids over which these flatness properties of S-acts are preserved under finite direct products. This thesis also consider the conditions when the products of S-acts have the above properties if and only if each component has the corresponding properties.