Generalized symmetric rings
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Generalized symmetric rings
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| Creator |
Kafkas, G.
Ungor, B. Halicioglu, S. Harmanci, A. |
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| Description |
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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| Date |
2019-06-15T20:29:23Z
2019-06-15T20:29:23Z 2011 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/154759 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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