Direct sums of projective modules as direct summaots of their direct product

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On the endomorphism ring of a free module

This survey covers material inReferativnyi Zhurnal Matematika and is a continuation of A. V. Mikhalev's survey in Algebra. Topology. Geometry, Vol. 12 (Itogi Nauki i Tekhniki (1974)). Papers on endomorphism rings of modules over associative rings and on lattices of submodules are considered.

Endomorphism rings of modules and lattices of submodules

Suppose is some property of modules. Let denote the class of rings over which all modules possess property . The main theorem of this paper answers the following question for a rather extensive class of properties ; what must the property of modules be in order that if and only if , for any free -module ? Among the corollaries are many well-known theorems relating properties of the ring and the rings , and also a number of new results of similar type.Bibliography: 35 items.

Endomorphism rings of free modules

We find a condition on the endomorphism rings of free right R-modules which is equivalent to R being a right perfect ring. We also obtain different characterizations of right perfect rings with nonzero right annihilators of the proper left ideals of finite descent. Bibliography: 15 items.

Endomorphism rings of free modules over perfect rings

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