Gray, Andrew Jeremy (1984) Centres and invertible ideals of Noetherian rings. PhD thesis, University of Warwick.

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Abstract

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).

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Rings (Algebra), Noetherian rings, Commutative rings
Official Date:	January 1984
Dates:	Date Event January 1984 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hajarnavis, C. R.
Format of File:	pdf
Extent:	v, 111 leaves
Language:	eng

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