Generalized symmetric rings
In this paper, we introduce a class of rings which is a generalization of symmetric rings. Let R be a ring with identity. A ring R is called central symmetric if for any a, b,c∈R, abc=0 implies bac belongs to the center of R. Since every symmetric ring is central symmetric, we study sufficient c...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2011 |
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| 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/123456789/154759 |
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| Cite this: | Generalized symmetric rings / G. Kafkas, B. Ungor, S. Halicioglu, A. Harmanci // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 72–84. — Бібліогр.: 21 назв. — англ. |
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Kafkas, G. Ungor, B. Halicioglu, S. Harmanci, A. 2019-06-15T20:29:23Z 2019-06-15T20:29:23Z 2011 Generalized symmetric rings / G. Kafkas, B. Ungor, S. Halicioglu, A. Harmanci // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 72–84. — Бібліогр.: 21 назв. — англ. 1726-3255 2010 Mathematics Subject Classification:13C99, 16D80, 16U80 https://nasplib.isofts.kiev.ua/handle/123456789/154759 In this paper, we introduce a class of rings which is a generalization of symmetric rings. Let R be a ring with identity. A ring R is called central symmetric if for any a, b,c∈R, abc=0 implies bac belongs to the center of R. Since every symmetric ring is central symmetric, we study sufficient conditions for central symmetric rings to be symmetric. We prove that some results of symmetric rings can be extended to central symmetric rings for this general settings. We show that every central reduced ring is central symmetric, every central symmetric ring is central reversible, central semmicommutative, 2-primal, abelian and so directly finite. It is proven that the polynomial ring R[x] is central symmetric if and only if the Laurent polynomial ring R[x,x−1] is central symmetric. Among others, it is shown that for a right principally projective ring R, R is central symmetric if and only if R[x]/(xn) is central Armendariz, where n≥2 is a natural number and (xn) is the ideal generated by xn en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Generalized symmetric rings Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Generalized symmetric rings |
| spellingShingle |
Generalized symmetric rings Kafkas, G. Ungor, B. Halicioglu, S. Harmanci, A. |
| title_short |
Generalized symmetric rings |
| title_full |
Generalized symmetric rings |
| title_fullStr |
Generalized symmetric rings |
| title_full_unstemmed |
Generalized symmetric rings |
| title_sort |
generalized symmetric rings |
| author |
Kafkas, G. Ungor, B. Halicioglu, S. Harmanci, A. |
| author_facet |
Kafkas, G. Ungor, B. Halicioglu, S. Harmanci, A. |
| publishDate |
2011 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
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Інститут прикладної математики і механіки НАН України |
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Article |
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In this paper, we introduce a class of rings which is a generalization of symmetric rings. Let R be a ring with identity. A ring R is called central symmetric if for any a, b,c∈R, abc=0 implies bac belongs to the center of R. Since every symmetric ring is central symmetric, we study sufficient conditions for central symmetric rings to be symmetric. We prove that some results of symmetric rings can be extended to central symmetric rings for this general settings. We show that every central reduced ring is central symmetric, every central symmetric ring is central reversible, central semmicommutative, 2-primal, abelian and so directly finite. It is proven that the polynomial ring R[x] is central symmetric if and only if the Laurent polynomial ring R[x,x−1] is central symmetric. Among others, it is shown that for a right principally projective ring R, R is central symmetric if and only if R[x]/(xn) is central Armendariz, where n≥2 is a natural number and (xn) is the ideal generated by xn
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154759 |
| citation_txt |
Generalized symmetric rings / G. Kafkas, B. Ungor, S. Halicioglu, A. Harmanci // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 72–84. — Бібліогр.: 21 назв. — англ. |
| work_keys_str_mv |
AT kafkasg generalizedsymmetricrings AT ungorb generalizedsymmetricrings AT halicioglus generalizedsymmetricrings AT harmancia generalizedsymmetricrings |
| first_indexed |
2025-12-07T19:48:05Z |
| last_indexed |
2025-12-07T19:48:05Z |
| _version_ |
1850880174416986112 |