This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Fall 2009 MAT 322: ALGEBRA WITH GALOIS THEORY PROBLEM SET #8 Week #9: November 23rd  November 29th. (Thanksgiving week) Topics : Perfect fields, Galois extensions, field automorphisms, the Galois group. Read : FGT [2228] Problems due Friday, December 4th, at 4:00 pm in Martin Luus mailbox: Problem 1 : Let F be a field of characteristic p > , and fix an algebraic closure F . For each k > , show that the following subset is a subfield, F p k = { x F : x p k F } F. Let F per be the union of all these subfields. Show that F per is the smallest perfect subfield of F , containing F . That is, the perfect closure of F in F . Problem 2 : Let E/F be a finite extension, and assume E is a perfect field. Show that F is perfect. Is this true in general for algebraic extensions? Problem 3 : Show that ( F per : F ) is infinite if F is imperfect. Problem 4 : Let F be a field, and fix an algebraic closure F . Let F sep be the set of all F such that Irr...
View Full
Document
 '09
 CLAUSSORENSEN
 Algebra

Click to edit the document details