If where a is the image of a under the canonical epimorphism z z P .
Question:
If
where a̅ is the image of a under the canonical epimorphism z → zP.
(a) If ∫ is monic and /is irreducible in Zp[x] for some prime p, then f is irreducible in Z[x].
(b) Give an example to show that (a) may be false if ∫ is not monic.
(c) Extend (a) to polynomials over a unique factorization domain.
Transcribed Image Text:
f=Σax Z[x] and p is prime, let f= Σ a₁x¹ €Z₂[x],
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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