HW_handout_2 - 2 ⊂ I 3 ⊂ ··· be an ascending chain...

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Modern Algebra II Spring 2007 Factorization Exercise 1. Let D be an integral domain. Prove that if p 1 , p 2 , . . . , p m , q 1 , q 2 , . . . , q n D ( m, n Z + ) are primes and p 1 p 2 ··· p m = q 1 q 2 ··· q n then m = n and, after possibly reordering, p i and q i are associates for i = 1 , 2 , . . . , m . [ Suggestion: Induct on m .] Exercise 2. Let R be a ring and let I 1 I
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Unformatted text preview: 2 ⊂ I 3 ⊂ ··· be an ascending chain of ideals in R and let I = ∞ [ j =1 I j . a. Prove that I is an ideal in R . b. If R has an identity and each I j is proper, prove that I is also proper. Exercise 3. Page 335, # 38 Exercise 4. Page 340, # 24 1...
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This note was uploaded on 02/29/2012 for the course MATH 4363 taught by Professor Ryandaileda during the Spring '07 term at Trinity University.

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