Generalized pseudoinjectivity
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.
scientific article; zbMATH DE number 4114829
scientific article