ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this articl...
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| Format: | Article |
| Language: | English |
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Shahrood University of Technology
2015-02-01
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| Series: | Journal of Algebraic Systems |
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| Online Access: | http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdf |
| _version_ | 1818061621993406464 |
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| author | Mohammad Habibi |
| author_facet | Mohammad Habibi |
| author_sort | Mohammad Habibi |
| collection | DOAJ |
| description | Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse skew power series type. We determine the radicals of theinverse skew Laurent series ring $R((x^{-1};alpha))$, in terms ofthose of $R$. We also prove that several properties transfer between$R$ and the inverse skew Laurent series extension$R((x^{-1};alpha))$, in case $R$ is a strongly Armendariz ring ofinverse skew power series type. |
| first_indexed | 2024-12-10T13:51:14Z |
| format | Article |
| id | doaj.art-cde798de49ba4e9a989f89e1f21bd2a7 |
| institution | Directory Open Access Journal |
| issn | 2345-5128 2345-511X |
| language | English |
| last_indexed | 2024-12-10T13:51:14Z |
| publishDate | 2015-02-01 |
| publisher | Shahrood University of Technology |
| record_format | Article |
| series | Journal of Algebraic Systems |
| spelling | doaj.art-cde798de49ba4e9a989f89e1f21bd2a72022-12-22T01:46:11ZengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2015-02-012210912410.22044/jas.2015.360360ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGSMohammad Habibi0Department of Mathematics, University of TafreshLet $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse skew power series type. We determine the radicals of theinverse skew Laurent series ring $R((x^{-1};alpha))$, in terms ofthose of $R$. We also prove that several properties transfer between$R$ and the inverse skew Laurent series extension$R((x^{-1};alpha))$, in case $R$ is a strongly Armendariz ring ofinverse skew power series type.http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdfInverse skew power series extensionsRadical propertySemicommutative rings |
| spellingShingle | Mohammad Habibi ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS Journal of Algebraic Systems Inverse skew power series extensions Radical property Semicommutative rings |
| title | ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS |
| title_full | ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS |
| title_fullStr | ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS |
| title_full_unstemmed | ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS |
| title_short | ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS |
| title_sort | on annihilator properties of inverse skew power series rings |
| topic | Inverse skew power series extensions Radical property Semicommutative rings |
| url | http://jas.shahroodut.ac.ir/article_360_3c473d1d286abc25947c292a6b305359.pdf |
| work_keys_str_mv | AT mohammadhabibi onannihilatorpropertiesofinverseskewpowerseriesrings |