| Let S be a monoid and A be a right S-acts.Firstly,we study the flatness properties of S-acts when the monoid form is S=G(?)I,and including GP-flatness,strong torsion free,Condition(PWP),Condition(EP),Condition(G-PWP),Condition(PWPE),and C(P)acts,etc..These flatness properties are discussed as the relation between I1-act and S-acts.Some examples are given which do not satisfy the flatness properties of the above relations.Secondly,for any monoid S,let A be the right S-acts and B be the proper subact of A.In this paper,we also studied the general amalgamated coproduct A(?)B A meet the Condition(G-PWP),Condition(PW PE),Condition(W),K-separation properties of equivalent characterizations.The relationship between right S-acts A and the general amalgamated coproduct A(?)B A is explored.Finally,the related applications are given. |
