Answered: Let R=Z[X], and let I be the ideal…

Let R=Z[X], and let I be the ideal generated by x3 +2x. Find integers a, b, and c such that in R/I we have I+x5+x6=I+a+bx+cx2.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 16E

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Question

16.2.4

Let R=Z[X], and let I be the ideal generated by x³ +2x. Find integers a, b, and c such that in R/I we have I+x⁵+x⁶=I+a+bx+cx².

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