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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 829–836
(Mi smj1881)
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This article is cited in 1 scientific paper (total in 1 paper)
On the normal ideals of exchange rings
D. Lua, T. Wub a School of Mathematical Sciences, Soochow University
b Department of Mathematics, Shanghai Jiao Tong University
Abstract:
An ideal $I$ of a ring $R$ is called normal if all idempotent elements in $I$ lie in the center of $R$. We prove that if $I$ is a normal ideal of an exchange ring $R$ then: (1) $R$ and $R/I$ have the same stable range; (2) $V(I)$ is an order-ideal of the monoid $C(\operatorname{Specc}(R),N)$, where $\operatorname{Specc}(R)$ consists of all prime ideals $P$ such that $R/P$ is local.
Keywords:
exchange ring, normal, $\operatorname{Specc}(R)$, monoid, order-ideal.
Received: 08.11.2006
Citation:
D. Lu, T. Wu, “On the normal ideals of exchange rings”, Sibirsk. Mat. Zh., 49:4 (2008), 829–836; Siberian Math. J., 49:4 (2008), 663–668
Linking options:
https://www.mathnet.ru/eng/smj1881 https://www.mathnet.ru/eng/smj/v49/i4/p829
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