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(Specc(R), N), where Specc(R) consists of all prime ideals P such that R/P is local.
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Original Russian Text Copyright © 2008 Lu D. and Wu T.
The authors were supported by the National Natural Science Foundation of China (Grant 10671122), partially by the Collegial Natural Science Research Program of Education Department of Jiangsu Province (Grant 07KJD110179), and partially by the Natural Science Foundation of Shanghai (Grant 06ZR14049).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 4, pp. 829–836, July–August, 2008.
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Lu, D., Wu, T. On the normal ideals of exchange rings. Sib Math J 49, 663–668 (2008). https://doi.org/10.1007/s11202-008-0063-3
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DOI: https://doi.org/10.1007/s11202-008-0063-3