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10. Prove that the ring Z[w] is a UFD, where w²+w+1=0. [Hint: As in the previous question, prove that Z[w] has a division algorithm with respect to the function "absolute value squared" v(a + bw) = (a + bw) (a + bw²) = a² - ab+b².]

10. Prove that the ring Z[w] is a UFD, where w²+w+1=0. [Hint: As in the previous question, prove that Z[w] has a division algorithm with respect to the function "absolute value squared" v(a + bw) = (a + bw) (a + bw²) = a² - ab+b².]

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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10. Prove that the ring Z[w] is a UFD, where w²+w+1=0. [Hint: As in the previous question, prove that Z[w] has a division algorithm with respect to the function "absolute value squared" v(a + bw) = (a + bw) (a + bw²) = a² - ab+b².]
Transcribed Image Text:10. Prove that the ring Z[w] is a UFD, where w²+w+1=0. [Hint: As in the previous question, prove that Z[w] has a division algorithm with respect to the function "absolute value squared" v(a + bw) = (a + bw) (a + bw²) = a² - ab+b².]
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