RINGS WITH ENOUGH INVERTIBLE IDEALS AND THEIR DIVISOR CLASS GROUPS

Akalan E.

COMMUNICATIONS IN ALGEBRA, vol.37, no.12, pp.4374-4390, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 12
  • Publication Date: 2009
  • Doi Number: 10.1080/00927870902829031
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4374-4390
  • Hacettepe University Affiliated: Yes

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.