Let R b e the ring of omplex numb ers C. Show that the map φ : R → Rgiven by φ(z) = ¯z (where ¯z denotes the omplex onjugate of z) is a ringisomorphism.

Question

Let R b e the ring of omplex numb ers C. Show that the map φ : R → Rgiven by φ(z) = ¯z (where ¯z denotes the omplex onjugate of z) is a ringisomorphism.
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Solution 1

To show that the map φ : R → R given by φ(z) = z̄ is a ring isomorphism, we need to show that it is a bijective ring homomorphism.

  1. Ring homomorphism: A function φ : R → R is a ring homomorphism if for all a, b in R, the following two conditions hold:

    i. φ(a + b) = φ(a) + φ(b)

    ii. φ(a Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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