ProblemSet11 - Q [ x ] / ( p ( x )). 6. Let F = Z 2 and let...

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

View Full Document Right Arrow Icon
Homework 11 Due: NEVER 1. Describe the elements of Q ( 3 5). Justify carefully using an appropriate theorem. 2. Show Q ( 2 , 3) = Q ( 2 + 3). 3. Find the splitting field for x 3 - 1 over Q . Express your answer in the form Q ( a ). 4. Find the splitting field for x 4 + 1 over Q . 5. Find a polynomial p ( x ) in Q [ x ] so that Q ( p 1 + 5) is isomorphic to
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Q [ x ] / ( p ( x )). 6. Let F = Z 2 and let f ( x ) = x 3 + x +1 F [ x ]. Suppose a is a zero of f ( x ) in some extension of F . How many elements does F ( a ) have? Express each member of F ( a ) in terms of a . Write out a complete multiplication table for F ( a )....
View Full Document

Ask a homework question - tutors are online