On Reduced archimedean skew power series rings

In this paper, we prove that if $R$ is an Archimedean reduced ring and satisfy ACC on annihilators, then $R[[x]]$ is also an Archimedean reduced ring. More generally we prove that if $R$ is a right Archimedean ring satisfying the \emph{ACC} on annihilators and $\alpha$ is a rigid automorphism of $R$, then the skew power series ring $R[[x;\alpha ]]$ is right Archimedean reduced ring. We also provide some examples to justify the assumptions we made to obtain the required result.