hw9 - R be a commutative ring, let I R , and let M / I be a...

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Math 4124 Monday, April 18 Ninth Homework Due 2:30 p.m., Monday April 25 1. Section 7.3, Exercise 10 (a),(b),(c),(d) on page 248. (3 points) 2. Section 7.3, Exercise 34 on page 250. (For (d) write 1 = i + j and if x I J , consider x = xi + x j .) (3 points) 3. Prove that the polynomial ring R [ x ] has a maximal ideal M such that R [ x ] / M = C . (2 points) 4. Let
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Unformatted text preview: R be a commutative ring, let I R , and let M / I be a maximal ideal of R / I . Prove that M is a maximal ideal of R . (2 points) 5. Give an example of a commutative ring R with a 1 and a nonzero prime ideal P of R such that P = P 2 . (2 points) (5 problems, 12 points altogether)...
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This note was uploaded on 01/02/2012 for the course MATH 4124 taught by Professor Staff during the Spring '08 term at Virginia Tech.

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