{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW9_322_F09

# HW9_322_F09 - Fall 2009 MAT 322 ALGEBRA WITH GALOIS THEORY...

This preview shows pages 1–2. Sign up to view the full content.

Fall 2009 MAT 322: ALGEBRA WITH GALOIS THEORY PROBLEM SET #9 Week #10: November 30th - December 6th. Topics : Dedekind’s inequality, finite subgroups of F × are cyclic, primitive element theorem, Artin’s theorem, Galois criteria, the Galois correspondence, ex x 3 - 2. Read : FGT [29-34] and [36-42] Problems due Friday, December 11th, at 4:00 pm in Martin Luu’s mailbox: Problem 1 : Let E be the splitting field of x 4 - 4 x 2 + 2 Q [ x ] . Describe the automorphisms of E , and find a generator for the group Gal( E/ Q ) . Problem 2 : Find a primitive element (over Q ) for each subfield of Q ( ζ 13 ) , and draw a diagram showing all inclusions among these subfields, and find their relative degrees. Do the same for Q ( ζ 17 ) . What is noteworthy? Problem 3 : For an odd prime p , we let ( · p ) denote the Legendre symbol. That is, it is the unique non-trivial group homomorphism · p : ( Z /p Z ) × → {± 1 } , a a p . For each integer n , we consider the Gauss sum g n defined as follows: g n df = p - 1 a =1 ( a p ) e 2 πian/p .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

HW9_322_F09 - Fall 2009 MAT 322 ALGEBRA WITH GALOIS THEORY...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online