ON (m, n)-INJECTIVITY OF MODULES

Abstract

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-injective if every right R-homomorphism from an n-generated submodule of R^m to M extends to one from R^m to M. This definition unifies several definitions on generalizations of injectivity of modules. The aim of this paper is to investigate properties of the (m, n)-injective modules. Various results are developed, many extending known results.

ACKNOWLEDGMENTS

This work was carried out during a visit of the second author to Memorial University of Newfoundland, St. John's, Canada. It is the second author's pleasure to thank the Department of Mathematics and Statistics of Memorial University for its kind hospitality. The research was supported in part by the National Natural Science Foundation of China and the Natural Sciences and Engineering Research Council of Canada.