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Title: Centres and invertible ideals of Noetherian rings
Author: Gray, Andrew Jeremy
ISNI:       0000 0001 3512 1740
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1984
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This thesis may be divided into two sections. In Chapter 4 we investigate the properties of the Rees ring with respect to an invertible ideal of a non-commutative ring. The technique developed demonstrates the close relationship between invertible ideals and principal ideals. We apply it to derive straightforward proofs of the Invertible Ideal Theorem (Theorem 4.7) and certain results on completions (Chapter 5). The second half comprises Chapter 6, and concerns Noetherian local rings of finite global dimension which are integral over their centres. Such a ring is shown to be a maximal order, i.e. is "integrally closed". Earlier chapters deal with the requisite background material which is mostly (but not all) contained in the literature. Greater detail will be found in the introductory chapter (Chapter 1).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics