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On finiteness of multiplication modules
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Koohy, Hashem (2008) On finiteness of multiplication modules. Acta Mathematica Hungarica, Vol.118 (No.1-2). pp. 1-7. doi:10.1007/s10474-007-6136-0 ISSN 0236-5294.
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Official URL: http://dx.doi.org/10.1007/s10474-007-6136-0
Abstract
Our main aim in this note, is a further generalization of a result due to D. D. Anderson, i.e., it is shown that if R is a commutative ring, and M a multiplication R-module, such that every prime ideal minimal over Ann (M) is finitely generated, then M contains only a finite number of minimal prime submodules. This immediately yields that if P is a projective ideal of R, such that every prime ideal minimal over Ann (P) is finitely generated, then P is finitely generated. Furthermore, it is established that if M is a multiplication R-module in which every minimal prime submodule is finitely generated, then R contains only a finite number of prime ideals minimal over Ann (M).
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): | Modules (Algebra), Multiplication, Modular arithmetic | ||||
Journal or Publication Title: | Acta Mathematica Hungarica | ||||
Publisher: | Springer ; Akademiai Kiado Rt | ||||
ISSN: | 0236-5294 | ||||
Official Date: | January 2008 | ||||
Dates: |
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Volume: | Vol.118 | ||||
Number: | No.1-2 | ||||
Number of Pages: | 7 | ||||
Page Range: | pp. 1-7 | ||||
DOI: | 10.1007/s10474-007-6136-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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