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Algebra and Discrete Mathematics, 2011, том 12, выпуск 2, страницы 72–84
(Mi adm130)
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Эта публикация цитируется в 11 научных статьях (всего в 11 статьях)
RESEARCH ARTICLE
Generalized symmetric rings
G. Kafkasa, B. Ungora, S. Halıcıoglua, A. Harmancib a Department of Mathematics, Ankara University,
Turkey
b Department of Mathematics, Hacettepe University, Turkey
Аннотация:
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 $a$, $b, c\in R$, $abc = 0$ 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 $R[x]/(x^n)$ is central Armendariz, where $n\geq 2~$ is a natural number and $(x^n)$ is the ideal generated by $x^n$.
Ключевые слова:
symmetric rings, central reduced rings, central symmetric rings, central reversible rings, central semicommutative rings, central Armendariz rings, 2-primal rings.
Поступила в редакцию: 11.07.2011 Исправленный вариант: 18.12.2011
Образец цитирования:
G. Kafkas, B. Ungor, S. Hal{\i}c{\i}oglu, A. Harmanci, “Generalized symmetric rings”, Algebra Discrete Math., 12:2 (2011), 72–84
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm130 https://www.mathnet.ru/rus/adm/v12/i2/p72
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