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ehrenfest
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[SOLVED] show a matrix ring is simple
Show that the matrix ring M_2(Z_2) is a simple ring; that is, M_2(Z_2) has no proper nontrivial ideals.
In my book M_2(Z_2) is the ring of 2 by 2 matrices whose elements are in Z_2.
I wrote down all of the elements of the ring. I stared at them for awhile and I couldn't think of anything to do. We want to show that if H is a nontrivial additive subgroup of the ring, then M_2(Z_2) H must equal M_2(Z_2). But how...
Homework Statement
Show that the matrix ring M_2(Z_2) is a simple ring; that is, M_2(Z_2) has no proper nontrivial ideals.
In my book M_2(Z_2) is the ring of 2 by 2 matrices whose elements are in Z_2.
Homework Equations
The Attempt at a Solution
I wrote down all of the elements of the ring. I stared at them for awhile and I couldn't think of anything to do. We want to show that if H is a nontrivial additive subgroup of the ring, then M_2(Z_2) H must equal M_2(Z_2). But how...