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 $α$ is a rigid automorphism of $R$, then the skew power series ring $R[[x;α]]$ is right Archimedean reduced ring. We also provide some examples to justify the assumptions we made to obtain the required result.

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