home6 - have to show that either I = M or I = R . If it was...

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MATH 4107 HOMEWORK #6 DUE: April 23, 2010 Work the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for grading. Write LEGIBLY on the FRONT side of the page only, and STAPLE your pages together. 1. Problem 4.2 #8. 2. Problem 4.4 #6. Note: You may assume without proof that R is a subring of R , but be sure to show that M is an ideal in R . Hints for showing M is maximal: Suppose that I is an ideal such that M I R . You
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Unformatted text preview: have to show that either I = M or I = R . If it was the case that I = M then youre done, so suppose that I n = M . In this case, there exists some element k + 2 that belongs to I but not to M . Consider ( k + 2) ( k 2); this belongs to what ideal? And then write k = 5 m + r and = 5 n + s where r and s are the remainders after dividing by 5. 3. Problem 4.4 #7. With M and R as in Problem 4.4 #6, show that R/M is a eld having 25 elements. 4. Problem 4.5 #14, part a only. 1...
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This note was uploaded on 08/25/2011 for the course MATH 4107 taught by Professor Staff during the Spring '10 term at University of Florida.

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