If 

where a̅ is the image of a under the canonical epimorphism z → z_P.

(a) If ∫ is monic and /is irreducible in Z_p[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],