Unique representation domains, II

dc.creatorBaghdadi, Said El
dc.creatorGabelli, Stefania
dc.creatorZafrullah, Muhammad
dc.date2008-07-21
dc.date.accessioned2026-07-07T09:51:51Z
dc.date.available2026-07-07T09:51:51Z
dc.descriptionGiven 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.description21 pages
dc.identifierhttps://arxiv.org/abs/0807.3295
dc.identifierhttp://arxiv.org/abs/0807.3295
dc.identifierJ. Pure Appl. Algebra, 212 (2008), 376-392
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165392
dc.subjectCommutative Algebra
dc.subject13A15, 13F05, 13G05
dc.titleUnique representation domains, II
dc.typetext

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