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3 Z3 [x]/(x² + 1) (not reduced mo coefficients did modulo 2).

3 Z3 [x]/(x² + 1) (not reduced mo coefficients did modulo 2).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using methods like we used in class when learning about factor rings, consider this factor ring Z3 [x]/(x² + 1) (note this is now with coefficients reduced modulo 3, in class we did modulo 2). Part a Compute a minimal set of coset representatives of the factor ring (like we did in class) and write down the multiplication and addition table for this ring. Part b Prove or disprove: (x² + 1) C Z3 [x] is a maximal ideal of this ring.
Transcribed Image Text:Using methods like we used in class when learning about factor rings, consider this factor ring Z3 [x]/(x² + 1) (note this is now with coefficients reduced modulo 3, in class we did modulo 2). Part a Compute a minimal set of coset representatives of the factor ring (like we did in class) and write down the multiplication and addition table for this ring. Part b Prove or disprove: (x² + 1) C Z3 [x] is a maximal ideal of this ring.
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