On reduced archimedean skew power series rings

In this paper, we prove that if R is an Arc himedean reduced ring and satisfy ACC onannihilators, then R[[x]] is also an Archimedean reduced ring. More generally, we provethat if R is a right Archimedean ring satisfying the ACC on annihilators and α is arigid automorphism of R, then the skew pow er series ring R[[x; α]] is right Archimedeanreduced ring. We also provide some examples to justify the assumptions we made toobtain the required result