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Akalan, Evrim (2009) Rings with enough invertib;e ideals and their divisor class groups. Communications in Algebra, Vol.37 (No.12). pp. 4374-4390. doi:10.1080/00927870902829031
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Official URL: http://dx.doi.org/10.1080/00927870902829031
Abstract
We investigate Noetherian maximal orders with enough invertible ideals and their two different divisor class groups. We show that in a Noetherian maximal order R with enough invertible ideals, every height 1 prime ideal P is maximal reflexive and R = boolean AND R-P boolean AND S, where P ranges over all height 1 prime ideals of R, and S is a simple Noetherian ring. We show that one of the class groups of R measures, to some extent, the lack of unique factorisation in the ring. We also investigate relations between the class groups of R and the divisor class group of the center of R. Examples are provided to illustrate our results.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Communications in Algebra | ||||
| Publisher: | Taylor & Francis Inc. | ||||
| ISSN: | 0092-7872 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.37 | ||||
| Number: | No.12 | ||||
| Number of Pages: | 17 | ||||
| Page Range: | pp. 4374-4390 | ||||
| DOI: | 10.1080/00927870902829031 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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