Correct answer: (C) Not an integral domain, but zero is its only nilpotent
Explanation
Factor X⁴+4=(X²−2X+2)(X²+2X+2). Both factors are distinct irreducible real quadratics. The Chinese remainder theorem gives a product of two fields, ℂ×ℂ. It has zero divisors, but an element is nilpotent only when both field components are zero. **C**.
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