Properties And Applications Of Rees Factor And Amalgam Of S-acts

Let S be a monoid,A an S-act and B any proper subact of A.In this paper,we study the general amalgam A(?)~BA.Taking A=S,B=I(I is the proper right ideal of S),then amalgam A(?)~BA is exactly a important tool A(I) to study the homological classification of momoids.In this paper,we discuss the equivalent characterizations of A(?)~BA satisfying condition(P),condition(E),torsion free,principally weakly flat,etc.,and completely generalize the corresponding results of A(I).In particular,some applications of general amalgam A(?)~BA are given,including the main tools for proving some important results.On the other hand,let A be any S-act and B is the proper subact of A.The general Rees factor A/B is studied for the first time and its flatness properties are discussed.If Ais S and B the proper right ideal of S,as applications,the main conclusions generalize the some known results of special Rees factor S/I.