(Fundamental theorem an module homomorphism) Let M, M' be R-mod-ules and f: M→ M' be an R-module homomorphism. Then Ker (f) is a submodule of M andM/Ker (f) Im (f). Equivalently, every homomorphic image of an R-module is isomorphic to somequotient module.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

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Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 19E: 19. a. Show that is isomorphic to , where the group operation in each of , and is addition. ...

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(Fundamental theorem an module homomorphism) Let M, M' be an R-module homomorphism. Then Ker (f) is a submodule quivalently, every homomorphic image of an R-module is isomorp