{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW5_322_F09

# HW5_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 #5 Week #5: October 19th - October 25th. Topics : Rings, fields, ideals, quotient rings, Chinese remainder theorem, integral domains, the field of fractions, PID’s, UFD’s, Euclidean domains, polynomials, power series, Laurent series, Eisenstein’s criterion. Read : FGT [1-6] (also a good idea to check out Lang’s Algebra , Ch. II) Problems due Friday, October 23rd, at 4:00 pm in Martin Luu’s mailbox: Problem 1 : Let F 4 be a field with four elements { 0 , 1 , x, y } . Write down the tables for addition and multiplication, hence showing F 4 is unique. Problem 2 : Let D n be the dihedral group of order 2 n , where n > 2 . Pick generators r and s such that r n = e , s 2 = e , and rs = sr - 1 . Write n as 2 m k , where k is odd. For each i m , show that Z i ( D n ) is generated by r n/ 2 i . Moreover, verify that Z i ( D n ) = Z m ( D n ) for every i m . Problem 3 : Let R be an integral domain: A commutative ring such that R = 0 , a, b R : ab = 0 a = 0 b = 0 .

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

HW5_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