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The failure of the Artin–Rees property for the Jacobson radical in prime Noetherian rings
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Braun, A. and Hajarnavis, C. R. (2011) The failure of the Artin–Rees property for the Jacobson radical in prime Noetherian rings. Journal of Algebra, Vol.348 (No.1). pp. 294-301. doi:10.1016/j.jalgebra.2011.09.023 ISSN 0021-8693.
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2011.09.023
Abstract
We provide an example of a prime Noetherian ring whose Jacobson radical fails to satisfy the Artin-Rees (AR) property on either side. The ring constructed is a finite module over its Noetherian centre. This settles a longstanding question.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Noncommutative rings, Noetherian rings | ||||
Journal or Publication Title: | Journal of Algebra | ||||
Publisher: | Academic Press Inc Elsevier Science | ||||
ISSN: | 0021-8693 | ||||
Official Date: | 15 December 2011 | ||||
Dates: |
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Volume: | Vol.348 | ||||
Number: | No.1 | ||||
Page Range: | pp. 294-301 | ||||
DOI: | 10.1016/j.jalgebra.2011.09.023 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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