This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: K ( a, b ) ∼ = K ( x, y ). (10 points) Name : Surname : (5) Find all prime numbers p such that there exist exactly 3 monic irreducible polynomials of degree 2 in F p [ x ]. (10 points) (6) Is f ( x ) := x 4 + 2 x 3 + 4 x 2 + 3 x + 2 ∈ F 5 [ x ] irreducible in F 5 [ x ]. (15 points) Name : Surname : (7) Describe the elements of the Felds F 7 [ √ 3] and F 7 [ √ 5]. Are these Felds isomorphic? If so, Fnd an isomorphism from F 7 [ √ 5] onto F 7 [ √ 3]. (15 points) (8) Consider the subfelds Q ( √ 2) and Q ( √ 3) oF R . Prove that, iF { α, β } is a Qlinearly independent subset oF Q ( √ 2), then { α, β } is Q ( √ 3)linearly independent. (10 points)...
View
Full
Document
This note was uploaded on 11/08/2011 for the course MATH 321 taught by Professor Ergenc during the Spring '11 term at Boğaziçi University.
 Spring '11
 ergenc
 Math

Click to edit the document details