Pseudo-Valuation Domains
| Author | Mohammed, Waleed Saleh Khamis. | |
|---|---|---|
| metadata.dc.contributor.department | UNIVERSITY OF BAHRAIN, College of Science, Department of Mathematics | |
| metadata.dc.date.accessioned | 2026-09-20T15:49:13Z | |
| Publication date | 2005 | |
| Degree level | Master | |
| Abstract | Abstract : Throughout this thesis, all rings are commutative with identity and the letter R denotes an integral domain with quotient field. K. Hedstrom and Houston [HH1] introduced the concept of Pseudo-valuation domain (PVD for short). The name "Pseudo-valuation" domain is justified by the fact that these rings share many ideal theoretical properties with the valuation rings to which they are closely related. The motivations for studying such a generalization of a valuation domain are diverse and meaningful [DF3]. PVD has been studied extensively in [HH2], [D2], [AN], [AD1], [B1], [DF2], [OK], [B5], [B2] and [B4]. This thesis is divided into three chapters. In chapter I, several characterizations of PVD are given in section 1. Sections 2 and 3 deal with the relationship between PVD and valuation domain, and that between PVD and associated valuation domain, respectively. Section 4 provides a new characterization of PVD using the notion of group of divisibility [AN1], [O]. Chapter II produces a beautiful way of constructing PVDs in section 1. Section 2 studies the overrings of a PVD, while section 3 investigates the relationship between PVD and Noetherian domains. Finally, section 4 introduces the notion of strong local homomorphism and how to relate PVDs to valuation domains through this notion Chapter III generalizes the study of PVD to the context of arbitrary integral domains by defining the notion of pseudo-valuation subring R in an integral domain S. This generalization provides two types of PVDs. Most of the concepts in chapters I and II are generalized in this chapter by a natural way | |
| metadata.dc.identifier.other | Drupal node 3854 | |
| metadata.dc.identifier.other | https://digitalrepository.uob.edu.bh/en/dar/pseudo-valuation-domains | |
| metadata.dc.identifier.uri | http://165.227.56.122/handle/123456789/6838 | |
| Language | en | |
| Link | https://digitalrepository.uob.edu.bh/en/_flysystem/fedora/2025-07/001332_pseudo-valuation_domains.pdf | |
| Subject | Rings "Algebra" -- Dissertations | |
| Subject | Valuation -- Mathematical models -- Dissertations | |
| Title | Pseudo-Valuation Domains | |
| Type | Master's Thesis | |
| College | College of Science | |
| Department | Mathematics |
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