Let MR be a finitely generated module over a ring R. Prove:(a) Every proper submodule of M is contained in a maximal sub-module of M.(b) Rad(M) is a small submodule of M.

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Answered: Let MR be a finitely generated module…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let MR be a finitely generated module over a ring R. Prove: (a) Every proper submodule of M is contained in a maximal sub- module of M. (b) Rad(M) is a small submodule of M.