Theorem 12. Let R is a commutative ring and re R,fe Hom (M, M'), then rf e HomRR(M, M') defined by (rf) (x) = rƒ (x) for all x e M and with this scalar multiplication the abeliangroup Hom(M, M') is an R-module.R

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Answered: Theorem 12. Let R is a commutative ring…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 5E: Examples 5 and 6 of Section 5.1 showed that P(U) is a commutative ring with unity. In Exercises 4...

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Theorem 12. Let R is a commutative ring and r e R,fe Hom (M, M'), then rfe. R M, M') defined by (rf) (x) = rf (x) for all x M and with this scalar multiplication the a oup Hom (M, M') is an R-module. R