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February 21st, 2013, 05:13 AM  #1 
Newbie 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? Thankyou 
February 21st, 2013, 03:48 PM  #2 
Member Joined: Jan 2013 Posts: 93 Thanks: 0  Re: Ring theory problem
I’ll 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 (don’t worry about reducing the coefficients mod 2 at this stage): Hence in . 
February 23rd, 2013, 07:42 AM  #3 
Newbie Joined: Feb 2013 Posts: 2 Thanks: 0  Re: Ring Theory Problem, Help highly appreciated!!
Thankyou very much! That was really helpful 

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