ON RINGS WHOSE REFLEXIVE IDEALS ARE PRINCIPAL


Akalan E.

COMMUNICATIONS IN ALGEBRA, vol.38, no.9, pp.3174-3180, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 9
  • Publication Date: 2010
  • Doi Number: 10.1080/00927870903164693
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3174-3180
  • Hacettepe University Affiliated: Yes

Abstract

We call a prime Noetherian maximal order R a pseudo-principal ring if every reflexive ideal of R is principal. This class of rings is a broad class properly containing both prime Noetherian pri-(pli) rings and Noetherian unique factorization rings (UFRs). We show that the class of pseudo-principal rings is closed under formation of n x n full matrix rings. Moreover, we prove that if R is a pseudo-principal ring, then the polynomial ring R[x] is also a pseudo-principal ring. We provide examples to illustrate our results.