Some decomposition properties of injective and pure-injective modules
Many results are known about injective modules, or generalisations thereof, in the category of modules over a ring. For example there are results concerning the expressibility of such modules as direct sums of indecomposable modules. The theme of this paper is to prove such results for injective objects, or more general objects, in a suitable category. For instance if \(M\) is a sigma-injective object and \(F\) is a CS subobject of \(M\), then \(F\) is a direct sum of indecomposable objects. Also in this categorical context a generalization is given of the Faith-Walker characterization of sigma-injective modules. The authors are thus able to give new proofs of, or to extend, some known results about generalizations of injective modules.
scientific article; zbMATH DE number 639568