A note on small rings
type: Item
instance of: scholarly article
title: A note on small rings
zbMATH Open document ID: 0633.13001
DOI: 10.1007/BF01951000
author: Mary Rayar
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: The author generalizes several results of the reviewer [Sitzungsber., Bayer. Akad. Wiss., Math.-Naturwiss. Kl. 1965, 185-199 (1966; Zbl 0207.327)] on Dedekind domains to finite direct sums \(R=R_ 1\oplus...\oplus R_ n\) of such. Among the proper commutative domains \(R_ i\) the Dedekind domains are characterized by the fact that R-modules are injective iff they coincide with their Jacobson radicals, or by the fact that finitely generated R-modules with zero socle are projective. The author uses some results on rings which are small (superfluous) modules (in their injective hulls).
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 16Nxx
zbMATH DE Number: 4029712
zbMATH Keywords: small module
zbMATH Keywords: small ring
zbMATH Keywords: projectivity
zbMATH Keywords: injectivity
zbMATH Keywords: Dedekind domains
zbMATH Keywords: Jacobson radicals
reviewed by: Bodo Pareigis
MaRDI profile type: Publication
cites work: Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
cites work: Homological properties of the ring of differential polynomials
cites work: Small Modules
cites work: Torsion-Free and Divisible Modules Over Non-Integral-Domains
full work available at URL: https://doi.org/10.1007/bf01951000
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description: scientific article; zbMATH DE number 4029712