Annihilator of Tensor Product of S-acts

Abstract

ForS-actsSM andUS,letAnn (U)={(m,m)∈M×M|u⊗m=

u ⊗ m for any u ∈ U}. Then US is called SM-faithful if Ann (U) is M

the identity relation on M . If US is S M -faithful for any S-act S M , then we call US completely faithful. The present paper discusses proer- ties of S M -faithful(completely faithful) S-acts. The structures of S M - faithful(completely faithful) right S-acts are characterized. Some related results are also obtained.