oct19 - ) = ( f ( x )) + g ( x ) . We use the division...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 5125 Wednesday, October 19 October 19, Ungraded Homework Exercise 9.2.1 on page 301 Let F be a field, let f ( x ) F [ x ] , and let bars denote passage to the quotient F [ x ] / ( f ( x )) . Prove that for each g ( x ) , there is a unique polynomial g 0 ( x ) of degree n - 1 (or g 0 = 0) such that g ( x ) = g 0 ( x ) . By definition, g ( x
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) = ( f ( x )) + g ( x ) . We use the division algorithm: there are unique poly-nomials q ( x ) and g ( x ) with either g = 0 or deg g < deg f such that g = q f + g . Then g ( x ) = g ( x ) and the result follows....
View Full Document

This note was uploaded on 01/02/2012 for the course MATH 5125 taught by Professor Palinnell during the Fall '07 term at Virginia Tech.

Ask a homework question - tutors are online