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Rings with enough invertib;e ideals and their divisor class groups

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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

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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:
DateEvent
2009Published
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

Data sourced from Thomson Reuters' Web of Knowledge

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