46. number of elements in the group aut (zao) 19 a (6) (c) 4 (d) 47. let f be a ficld, then which 1s correct stalenn (a) frj is unique factorization domain (b)

46. Number of elements in the group Aut (Zao) 19 A (6) (C) 4 (D) 47. Let F be a ficld, then which 1s correct stalenn (A) Frj is unique factorization domain (B) Fx) is Euclidean domaine (C) FrJ is principal ideal domain. (D) All of these 8. Let k De an intcgral domain in which every ideal has the 1orm a rae K) for some a in R. Then Ris a: 05) principal 1deal domnin (D) None of these (A) Euclidean dortiain (9unique 1actorization domain 49. Let F be a field and I be non-zero idcal in F e]. Then I g )tor some s)eF[F]. iff: (A) s()* 0 and g() is of minimum degree (B) s(7) 0 and g() is monic (C) s() is monic (D) Nonc of these 50. Which of the following is nbt correct ? (A) The ideal (x+1) is maximal in R |] (B) The ideal () is a prime ideal in Z [E) (C) The ideal (x) is a maximal ideal in Z [o] (0) None of these