Generalized pseudoinjectivity
type: Item
instance of: scholarly article
title: Generalized pseudoinjectivity
zbMATH Open document ID: 0681.16017
DOI: 10.1007/BF01762388
author: Josef Jirásko
author: Ladislav Bican
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1988-01-01T00:00:00Z
review text: The notion of pseudoinjective modules was introduced by \textit{G. M. Cukerman} [Mat. Zametki 7, 369-380 (1970; Zbl 0225.16016)] and some properties of these modules have been studied by \textit{L. Bican} [Comment. Math. Univ. Carol. 14, 295-303 (1973; Zbl 0259.16005)] and \textit{Y. Kurata} and \textit{H. Katayama} [Osaka J. Math. 13, 407-418 (1976; Zbl 0353.16007)] from the point of view of torsion theories. The purpose of the paper under review is to present the theory of generalized pseudoinjective modules. Several characterizations of these modules are presented. Modules pseudoinjective with respect to a pair of preradicals which generalize modules injective with respect to preradicals due to \textit{J. A. Beachy} [Pac. J. Math. 41, 313-327 (1972; Zbl 0217.340)] are also investigated. It is shown that these modules are obtained from the above general theory and that for some types of modules, there are certain connections between generalized pseudoinjectivity and some special preradicals such as Jacobson radical, prime radical and singular preradical. Some remarks concerning Morita equivalence and generalized pseudoinjectivity are also presented.
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 4114829
zbMATH Keywords: generalized pseudoinjective modules
zbMATH Keywords: preradicals
zbMATH Keywords: Jacobson radical
zbMATH Keywords: prime radical
zbMATH Keywords: singular preradical
zbMATH Keywords: Morita equivalence
reviewed by: Yoshiki Kurata
MaRDI profile type: Publication
cites work: A generalization of injectivity
cites work: Q5675856
cites work: Preradicals and injectivity
cites work: Corational extensions and pseudo-projective modules
cites work: Q4100641
cites work: Hereditary and cohereditary preradicals
cites work: Q4190777
cites work: A general concept of the pseudoprojective module
cites work: Q3941569
cites work: Torsion associated with duality
cites work: Q4200358
cites work: Q3919846
cites work: Q3919847
cites work: Generalized projectivity
cites work: When is the radical associated with a module a torsion?
cites work: On a generalization of QF-3' rings
cites work: Half-exact pre-radicals
cites work: Codivisible modules
cites work: On pseudo-injective modules and self-pseudoinjective rings
full work available at URL: https://doi.org/10.1007/bf01762388
OpenAlex ID: W3193222344
description: scientific article; zbMATH DE number 4114829