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February 23rd, 2013, 05:08 PM  #1 
Newbie Joined: Feb 2013 Posts: 3 Thanks: 0  A ring theory question. Any help greatly appreciated
I need help with the following problem: Let R be a nil ring, that is a ring in which for each element a in R there is a natural number n(a) such that a^(n(a)) = 0. Prove that the ring of 2x2 matrices with coefficients from R is also a nil ring. Any help greatly appreciated 
February 25th, 2013, 10:18 AM  #2 
Senior Member Joined: Feb 2013 Posts: 281 Thanks: 0  Re: A ring theory question. Any help greatly appreciated
It is obvious for me, maybe I am wrong. If you multiply a matrix with itself N times and the result is R, then R(i,j) is a sum of Nordered members. If N is big enough then all member will be zero. N = N1+N2+ ... + N[n*n]. If N is huge then one of them must be huge, i.e. bigger than its nilpotent condition requires.


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