Mathematics · Abstract Algebra
Suppose that the mapping f: &complex; → &complex; is the complex conjugation map defined by f(z) = z̄, so that f(2 + 3i) = 2 - 3i. Which of the following statements is correct regarding f as a ring mapping?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f is a group homomorphism but fails to be a ring homomorphism.
- 2f is a ring homomorphism (specifically, a ring automorphism).✓
- 3f is not a ring homomorphism because it does not preserve addition.
- 4(f(2 + 3i))2 ≠ (2 - 3i)2
Correct answer
f is a ring homomorphism (specifically, a ring automorphism).
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