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On reduced archimedean skew power series rings

Hamed Mousavi

Mathematics Department, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, Georgia 30313, US

E-mail Address: [email protected]

Corresponding author.

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Farzad Padashnik

Department of Pure Mathematics, Faculty of Mathematical Sciences, Isfahan University, Isfahan, Iran

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, and

Ayesha Asloob Qureshi

Faculty of Engineering and Natural Sciences, Sabancı University, Orta Mahalle, Tuzla 34956, Istanbul, Turkey

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https://doi.org/10.1142/S0219498822500426Cited by:0 (Source: Crossref)

Abstract

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 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.

Communicated by S. R. López-Permouth

Keywords:

AMSC: 16P70, 16P60, 13F10, 13J05

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