On partial skew Armendariz rings
In this paper we consider rings R with a partial action α of an infinite cyclic group G on R. We introduce the concept of partial skew Armendariz rings and partial α-rigid rings. We show that partial α-rigid rings are partial skew Armendariz rings and we give necessary and sufficient conditions f...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154760 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On partial skew Armendariz rings / W. Cortes // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 23–45. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862711123699040256 |
|---|---|
| author | Cortes, W. |
| author_facet | Cortes, W. |
| citation_txt | On partial skew Armendariz rings / W. Cortes // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 23–45. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | In this paper we consider rings R with a partial action α of an infinite cyclic group G on R. We introduce the concept of partial skew Armendariz rings and partial α-rigid rings. We show that partial α-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;α].

We also show that R[x;α] and R⟨x;α⟩ are not necessarily associative rings when R satisfies the concepts mentioned above.
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| first_indexed | 2025-12-07T17:28:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154760 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:28:35Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Cortes, W. 2019-06-15T20:35:14Z 2019-06-15T20:35:14Z 2011 On partial skew Armendariz rings / W. Cortes // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 23–45. — Бібліогр.: 39 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16S36; 16S35 https://nasplib.isofts.kiev.ua/handle/123456789/154760 In this paper we consider rings R with a partial action α of an infinite cyclic group G on R. We introduce the concept of partial skew Armendariz rings and partial α-rigid rings. We show that partial α-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;α].
 
 We also show that R[x;α] and R⟨x;α⟩ are not necessarily associative rings when R satisfies the concepts mentioned above. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On partial skew Armendariz rings Article published earlier |
| spellingShingle | On partial skew Armendariz rings Cortes, W. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154760 |
| work_keys_str_mv | AT cortesw onpartialskewarmendarizrings |