Modules with many direct summands
Let X be a class of modules which is closed under isomorphism and which contains the zero module. The author studies modules M such that all, or certain, factor modules of M belong to X. For instance it is shown that every factor of M by an essential submodule is Noetherian (has finite uniform dimension) if and only if M is the extension of a semi-simple module by a Noetherian module (by a module all of whose factors have finite uniform dimension). Also every submodule N of M is contained in a direct summand K of M with K/N Noetherian (of finite uniform dimension) if and only if M is the direct sum of a semi-simple module and a Noetherian module (and a module all of whose factors have finite uniform dimension). Similar results are proved about modules with Krull dimension. Consequences include results of the reviewer [in Q. J. Math., Oxf. II. Ser. 33, 65-69 (1982; Zbl 0443.16011)].
scientific article; zbMATH DE number 4152621