Mathematics · Abstract Algebra
Which of the following statements is true regarding algebraic structures?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The subset {f ∈ C[0, 1] : f(1/2) = 0} of the ring C[0, 1] of continuous functions from [0, 1] to ℜ is a prime ideal✓
- 2The ring of integers ℤ is not a principal ideal domain
- 3The value of the Euler φ function is odd for all integers n ≥ 3
- 4The polynomial ring ℜ[x1, ..., xn] is a Euclidean domain for all integers n ≥ 1
Correct answer
The subset {f ∈ C[0, 1] : f(1/2) = 0} of the ring C[0, 1] of continuous functions from [0, 1] to ℜ is a prime ideal
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