hw9 - R is a UFD(2 points 4 Section 9.2 Exercise 3 on page...

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Math 5125 Friday, October 21 Ninth Homework Due 9:05 a.m., Friday October 28 1. Section 8.3, Exercise 5 on page 293. (4 points) 2. Let R be an integral domain, let S be a multiplicatively closed subset of R which contains 1 but not 0, and let p be a prime of R . Prove that p / 1 is either a prime or a unit of S - 1 R . (2 points) 3. Let R be an integral domain in which every nonzero element is either a unit or a product of primes. Prove that
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Unformatted text preview: R is a UFD. (2 points) 4. Section 9.2, Exercise 3 on page 301. (2 points) 5. Let R be an integral domain and let P be a prime ideal of R . Prove or give a coun-terexample to each of the following statements. (a) If R is a PID, then R / P is also a PID. (b) If R is a UFD, then R / P is also a UFD. (3 points) (5 problems, 13 points altogether)...
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