3. a) Let J = (2) in the ring Z10. Define the set I as I = {re 10 | rt = 0 for every t = J}. Find the elements of I explicitly. b) Is the set / from part (a), an ideal? Justify your answer. c) Now, you need to prove the following result (in general). Prove: For any ideal / in a ring R, the set I described below is an ideal in R. I={r ER❘rt OR for every tЄ J}
3. a) Let J = (2) in the ring Z10. Define the set I as I = {re 10 | rt = 0 for every t = J}. Find the elements of I explicitly. b) Is the set / from part (a), an ideal? Justify your answer. c) Now, you need to prove the following result (in general). Prove: For any ideal / in a ring R, the set I described below is an ideal in R. I={r ER❘rt OR for every tЄ J}
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 18E: 18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is...
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