On partial skew Armendariz rings
In this paper we consider rings \(R\) with a partial action \(\alpha\) of an infinite cyclic group \(G\) on \(R\). We introduce the concept of partial skew Armendariz rings and partial \(\alpha\)-rigid rings. We show that partial \(\alpha\)-rigid rings are partial skew Armendariz rings and we giv...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/658 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | In this paper we consider rings \(R\) with a partial action \(\alpha\) of an infinite cyclic group \(G\) on \(R\). We introduce the concept of partial skew Armendariz rings and partial \(\alpha\)-rigid rings. We show that partial \(\alpha\)-rigid rings are partial skew Armendariz rings and we give necessary and sufficient conditions for \(R\) to be a partial skew Armendariz ring. We study the transfer of Baer property, a.c.c. on right annhilators property, right p.p. property and right zip property between \(R\) and \(R[x;\alpha]\).We also show that \(R[x;\alpha]\) and \(R\langle x;\alpha\rangle\) are not necessarily associative rings when \(R\) satisfies the concepts mentioned above. |
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