Gabriel dimension of graded rings. II
type: Item
instance of: scholarly article
title: Gabriel dimension of graded rings. II
zbMATH Open document ID: 0645.16017
DOI: 10.1016/0022-4049(88)90004-7
author: Constantin Năstăsescu
author: Serban Raianu
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: [Part I cf. Rend. Semin. Mat. Univ. Padova 71, 195-208 (1984; Zbl 0545.13006).] Let R be a graded ring of type Z. By using the notions of relative Krull and Gabriel dimension with respect to a Gabriel topology, the authors prove that a graded R-module having a graded Gabriel dimension must have a Gabriel dimension when regarded without grading, and give a relation between the two dimensions. As a consequence, a new simple proof of a result due to Gordon and Robson concerning the Gabriel dimension of polynomials, without the use of quotient categories and polynomial categories, is obtained.
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 4051831
zbMATH Keywords: relative Krull dimension
zbMATH Keywords: graded filter
zbMATH Keywords: graded ring
zbMATH Keywords: Gabriel topology
zbMATH Keywords: graded R-module
zbMATH Keywords: graded Gabriel dimension
zbMATH Keywords: Gabriel dimension of polynomials
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90004-7
OpenAlex ID: W2016476937
cites work: Q3222338
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cites work: Des catégories abéliennes
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cites work: Gabriel dimension of graded rings
cites work: Finiteness conditions for graded modules (Gr-\(\Sigma\) (\(\Delta\) )- injective modules)
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description: scientific article; zbMATH DE number 4051831