Unique representation domains, II
| dc.creator | Baghdadi, Said El | |
| dc.creator | Gabelli, Stefania | |
| dc.creator | Zafrullah, Muhammad | |
| dc.date | 2008-07-21 | |
| dc.date.accessioned | 2026-07-07T09:51:51Z | |
| dc.date.available | 2026-07-07T09:51:51Z | |
| dc.description | Given a star operation * of finite type, we call a domain R a *-unique representation domain (*-URD) if each *-invertible *-ideal of R can be uniquely expressed as a *-product of pairwise *-comaximal ideals with prime radical. When * is the t-operation we call the *-URD simply a URD. Any unique factorization domain is a URD. Generalizing and unifying results due to Zafrullah and Brewer-Heinzer, we give conditions for a *-ideal to be a unique *-product of pairwise *-comaximal ideals with prime radical and characterize *-URDs. We show that the class of URDs includes rings of Krull type, the generalized Krull domains introduced by El Baghdadi and weakly Matlis domains whose t-spectrum is treed. We also study when the property of being a URD extends to some classes of overrings, such as polynomial extensions, rings of fractions and rings obtained by the D+XD_S[X] construction. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0807.3295 | |
| dc.identifier | http://arxiv.org/abs/0807.3295 | |
| dc.identifier | J. Pure Appl. Algebra, 212 (2008), 376-392 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165392 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A15, 13F05, 13G05 | |
| dc.title | Unique representation domains, II | |
| dc.type | text |