ON RINGS WHOSE REFLEXIVE IDEALS ARE PRINCIPAL
COMMUNICATIONS IN ALGEBRA, cilt.38, sa.9, ss.3174-3180, 2010 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 9
- Basım Tarihi: 2010
- Doi Numarası: 10.1080/00927870903164693
- Dergi Adı: COMMUNICATIONS IN ALGEBRA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.3174-3180
- Hacettepe Üniversitesi Adresli: Evet
Özet
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.