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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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| 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| _version_ | 1856543312131915776 |
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| author | Cortes, Wagner |
| author_facet | Cortes, Wagner |
| author_sort | Cortes, Wagner |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:21:34Z |
| description | 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. |
| first_indexed | 2025-12-02T15:27:13Z |
| format | Article |
| id | admjournalluguniveduua-article-658 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:27:13Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6582018-04-04T09:21:34Z On partial skew Armendariz rings Cortes, Wagner partial actions, Armendariz rings, Baer rings and P.P rings 16S36; 16S35 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/658 Algebra and Discrete Mathematics; Vol 11, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/658/192 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | partial actions Armendariz rings Baer rings and P.P rings 16S36 16S35 Cortes, Wagner On partial skew Armendariz rings |
| title | On partial skew Armendariz rings |
| title_full | On partial skew Armendariz rings |
| title_fullStr | On partial skew Armendariz rings |
| title_full_unstemmed | On partial skew Armendariz rings |
| title_short | On partial skew Armendariz rings |
| title_sort | on partial skew armendariz rings |
| topic | partial actions Armendariz rings Baer rings and P.P rings 16S36 16S35 |
| topic_facet | partial actions Armendariz rings Baer rings and P.P rings 16S36 16S35 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/658 |
| work_keys_str_mv | AT corteswagner onpartialskewarmendarizrings |