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Does anyone have a reference for the elementary divisor theorem which states that for any $2\times2$ integer matrix $A$, there exist matrices $P$ and $Q$ in $SL(2,Z)$ such that $PAQ$ is a diagonal matrix ?

Thanks.

2 Answers 2

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I personally like the treatment Jacobson gives in his

N. Jacobson. Basic algebra. I. W. H. Freeman and Company, New York, 1974 and 1985.

Perhaps you might want to search for it.

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    Thanks. I learned it a long time ago but now I forgot how to prove it. – 2017-01-14
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    It's a nice algorithm indeed. And thanks! – 2017-01-14
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Called Smith Normal Form. One book is Integral Matrices by Newman.

https://en.wikipedia.org/wiki/Smith_normal_form