Annihilator of Tensor Product of S-acts

Abstract

For S-acts SM and US, letAnnM (U)={(m,m)∈ M ×M|u⊗m = u ⊗m for any u ∈ U}. ThenUS is called SM-faithful if AnnM (U) is the identity relation on M. If US is SM-faithful for any S-act SM, then we call US completely faithful. The present paper discusses proerties of SM-faithful(completely faithful) S-acts. The structures of SMfaithful(completely faithful) right S-acts are characterized. Some related results are also obtained.