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# hw7 - x be a nonnilpotent element of R y is nilpotent means...

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Math 5125 Wednesday, October 5 Seventh Homework Due 9:05 a.m., Friday October 14 1. Let m , n Z such that m ± ± n . Prove that Z / n Z m ( Z / n Z ) = Z / m Z as rings. (3 points) 2. Section 7.3, Exercise 35 on page 250. (2 points) 3. Section 7.4, Exercise 5 on page 256. (2 points) 4. Section 7.4, Exercise 11 on page 257. (2 points) 5. Let R be a commutative ring with a 1 and let
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Unformatted text preview: x be a nonnilpotent element of R ( y is nilpotent means y n = 0 for some positive integer n ). (a) Prove that there is an ideal P of R maximal with respect to the property x n / ∈ P for all n ∈ Z + . (b) Prove that P is a prime ideal of R . (3 points) (5 problems, 12 points altogether)...
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