My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
February 21st, 2013, 05:13 AM   #1
Joined: Feb 2013

Posts: 2
Thanks: 0

Ring Theory Problem, Help highly appreciated!!

Here is the problem:

Consider the factor ring F2[x]/<x^3 +x>

(a) List the elements of this ring and write out the Cayley tables for addition
and multiplication in this ring.
(b)Find the units and the ideals of this factor ring.

So far, I have found the elements to be {0, 1, x, x+1, x^2, x^2+1, x^2+x, x^2+x+1}, but I am struggling with the Cayley tables and the units and ideals.

Does anyone know how to find the solutions to these problems?

brisunimath is offline  
February 21st, 2013, 03:48 PM   #2
Joined: Jan 2013

Posts: 93
Thanks: 0

Re: Ring theory problem

Iíll do an example. Suppose you want to find and .

Addition is straightfoward: .

For multiplication, proceed as follows.

1. Multiply the terms out like ordinary polynomials (donít worry about reducing the coefficients mod 2 at this stage):
2. Divide by :
3. Finally reduce the coefficients of the remainder mod 2:

Hence in .
Crimson Sunbird is offline  
February 23rd, 2013, 07:42 AM   #3
Joined: Feb 2013

Posts: 2
Thanks: 0

Re: Ring Theory Problem, Help highly appreciated!!

Thankyou very much! That was really helpful
brisunimath is offline  

  My Math Forum > College Math Forum > Abstract Algebra

appreciated, highly, problem, ring, theory

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
looking for patterns in this highly difficult problem davedave Algebra 2 October 12th, 2013 12:11 PM
A ring theory question. Any help greatly appreciated chappyform Abstract Algebra 1 February 25th, 2013 10:18 AM
Ring Theory - 0a = a0 = 0 PeterMarshall Abstract Algebra 4 January 20th, 2012 01:31 AM
Simplified Explanation Of Algebraic Ring Theory Pythonic Abstract Algebra 12 July 13th, 2011 01:54 PM
Ring Theory Question (Typo?) mgfortes Abstract Algebra 6 February 13th, 2011 10:52 AM

Copyright © 2019 My Math Forum. All rights reserved.