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On generalized Dedekind prime rings
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Akalan, Evrim (2008) On generalized Dedekind prime rings. Journal of Algebra, Volume 320 (Number 7). pp. 2907-2916. doi:10.1016/j.jalgebra.2008.07.001 ISSN 0021-8693.
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2008.07.001
Abstract
Let R be a maximal order and A, B be R-ideals of R. Clearly (A B)* superset of B*A* is satisfied and if R is a Dedekind prime ring, the equality holds, i.e., (AB)* = B*A*. However, the equality is not true in general. In this paper, we answer the question: If R is a maximal order when is (A B)* = B*A* for all non-zero R-ideals of R? We call prime Noetherian maximal orders satisfying this property, generalized Dedekind prime rings. We give several characterizations of G-Dedekind prime rings and show that being a G-Dedekind prime ring is a Morita invariant. Moreover, we prove that if R is a PI G-Dedekind prime ring then the polynomial ring R[x] and the Rees ring R[Xt] associated to an invertible ideal X are also PI G-Dedekind prime rings. (c) 2008 Elsevier Inc. All rights reserved.
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): | Commutative rings, Ideals (Algebra) | ||||
Journal or Publication Title: | Journal of Algebra | ||||
Publisher: | Academic Press | ||||
ISSN: | 0021-8693 | ||||
Official Date: | 1 October 2008 | ||||
Dates: |
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Volume: | Volume 320 | ||||
Number: | Number 7 | ||||
Number of Pages: | 10 | ||||
Page Range: | pp. 2907-2916 | ||||
DOI: | 10.1016/j.jalgebra.2008.07.001 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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