Kindly answer correctly, Please show the necessary steps2a (a) Let R* be the multiplicative group of nonzero real numbers, R** be the multiplicative group ofpositive real numbers and ƒ : R* →→→ R** be defined by f(x) = x².(i) Check as to whether f is a homomorphism or not[Hint: first check as to whether f is well defined or not](ii) If f is a homomorphism, then find its kernel

Given that ℝ* be the multiplicative group of nonzero real numbers, ℝ** be the multiplicative group…

Answered: (a) Let R* be the multiplicative group…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 12E: Exercises 12. Prove that the additive group of real numbers is isomorphic to the multiplicative...

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