The Flatness And Localization Of S-acts

In this thesis, Some characterizations of monoids and local Properties of fractional acts are given by studying Condition (E? and fractional acts. In section 1, Some basic Concepts and results Concerned are introduced. In Section 2 we introduce Condition (F? Presented by Validis Laan in [2] , and investigate the relations between Condition (F? and Condition(E), At the same time, We give Some equivalent conditions of condition(E?. In section 3, we make Some Characterizations of acts which satisfy condition (F?, and prove that S is regular monoid if and only if all the left acts satisfy condition (F? is flat. In Section 4 , we discuss a class of monoids that is weakly flat acts are flat. In section 5, we introduce fractional acts and localization over acts, and give Some characterization of them.