Some constructions of rings
type: Item
instance of: scholarly article
title: Some constructions of rings
zbMATH Open document ID: 0532.16001
DOI: 10.1016/0022-4049(84)90089-6
author: Fred Van Oystaeyen
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: Starting from a Dedekind domain R and a fractional ideal I of R one may construct the so-called generalised Rees ring as follows: \[ \check R(I)=...\oplus I^{-n}\oplus...\oplus I^{-1}\oplus R\oplus I\oplus...\oplus I^ n\oplus... \] The concept of a generalised Rees ring underwent consequent generalisations both in the commutative case and in the non-commutative case and it turned out that these constructions of graded nature also have very nice ungraded properties. In constructing those rings, the author obtains new examples of Goldie rings, maximal orders, tame orders in the sense of R. Fossum, Krull orders in the PI case or the general case, and \(\nu\) HC-orders in the sense of H. Fujita or H. Marubayashi. Three major classes are considered: strong Rees rings, divisorial Rees rings, scaled Rees rings; in each of these classes particular attention is payed to the commutative case, the PI case and the general case.
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 3843934
zbMATH Keywords: generalised Rees ring
zbMATH Keywords: Goldie rings
zbMATH Keywords: maximal orders
zbMATH Keywords: tame orders
zbMATH Keywords: Krull orders
zbMATH Keywords: \(\nu\) HC-orders
zbMATH Keywords: strong Rees rings
zbMATH Keywords: divisorial Rees rings
zbMATH Keywords: scaled Rees rings
reviewed by: Constantin Năstăsescu
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90089-6
OpenAlex ID: W2153207568
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description: scientific article; zbMATH DE number 3843934