Kindly answer correctly, Please show the necessary steps4a (a) Let R be the ring of all continuous real valued functions on the closed interval [0, 1]. Prove thatthe map: R→→→ R defined by$(1) = f ² 1is a homomorphism of additve groups but NOT a ring homomorphismf(t)dt

Here R be the ring of all continuous real valued functions on the closed interval [0,1] We have to…

Answered: Let R be the ring of all continuous…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 14E: 14. Let be a ring with unity . Verify that the mapping defined by is a homomorphism.

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Let R be the ring of all continuous real valued functions on the closed interval [0, 1]. Prove that the map : R→→→→R defined by Þ(f) = f* f(t)dt is a homomorphism of additve groups but NOT a ring homomorphism