Tagged: binomial expansion
Problem 587
Let $A$ and $B$ be square matrices such that they commute each other: $AB=BA$.
Assume that $A-B$ is a nilpotent matrix.
Then prove that the eigenvalues of $A$ and $B$ are the same.
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Ring theory
by
Yu
· Published 04/02/2017
· Last modified 08/01/2017
Problem 360
Let $R$ be a commutative ring and let $I_1$ and $I_2$ be comaximal ideals. That is, we have
\[I_1+I_2=R.\]
Then show that for any positive integers $m$ and $n$, the ideals $I_1^m$ and $I_2^n$ are comaximal.
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