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(d) If R is not an integral domain, we only have that deg(p(x)q(x)) ≤ deg(p(x)) + deg(q(x)). Give an explicit example of a case where the inequality is strict, i.e. deg(p(x)q(x)) < deg(p(x)) + deg(q(x)). (Hint: take R to be a (non-integral-domain) ring with small cardinality. The smaller cardinality makes the example easier).

(d) If R is not an integral domain, we only have that deg(p(x)q(x)) ≤ deg(p(x)) + deg(q(x)). Give an explicit example of a case where the inequality is strict, i.e. deg(p(x)q(x)) < deg(p(x)) + deg(q(x)). (Hint: take R to be a (non-integral-domain) ring with small cardinality. The smaller cardinality makes the example easier).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Ring theory. (Polynomial ring) 

(d) If R is not an integral domain, we only have that deg(p(x)q(x)) ≤ deg(p(x)) + deg(q(x)). Give an explicit example of a case where the inequality is strict, i.e. deg(p(x)q(x)) < deg(p(x)) + deg(q(x)). (Hint: take R to be a (non-integral-domain) ring with small cardinality. The smaller cardinality makes the example easier).
Transcribed Image Text:(d) If R is not an integral domain, we only have that deg(p(x)q(x)) ≤ deg(p(x)) + deg(q(x)). Give an explicit example of a case where the inequality is strict, i.e. deg(p(x)q(x)) < deg(p(x)) + deg(q(x)). (Hint: take R to be a (non-integral-domain) ring with small cardinality. The smaller cardinality makes the example easier).
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