On reduced archimedean skew power series rings

Mousavi, Hamed and Padashnik, Farzad and Asloob Topaçoğlu, Ayesha (2022) On reduced archimedean skew power series rings. Journal of Algebra and Its Applications, 21 (3). ISSN 0219-4988 (Print) 1793-6829 (Online)

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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.
Item Type: Article
Uncontrolled Keywords: Annihilator; Ascending chain conditions for principal one-sided ideals; Generalized power series rings; Ordered monoids; Right (or left) Archimedean ring; Skew power series ring
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ayesha Asloob Topaçoğlu
Date Deposited: 31 Aug 2022 17:44
Last Modified: 31 Aug 2022 17:44
URI: https://research.sabanciuniv.edu/id/eprint/43588

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