consider op: R* → R+, q(x) = x²R* is the group of non-zero real numbers with respectto multiplication.R+ is the group of positive real numbers with respectto multiplication.Show that is an onto (surjective)homomorphism.

We show that the function φ: ℝ* → ℝ+ defined by φ(x) = x2 is an onto (surjective) homomorphism, we…

Answered: consider op: R* → R+, q(x) = x² R* is…

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 11E: 11. Show that defined by is not a homomorphism.

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consider op: R* → R+, q(x) = x² R* is the group of non-zero real numbers with respect to multiplication. R+ is the group of positive real numbers with respect to multiplication. Show that is an onto (surjective) homomorphism.