Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $R$ be an euclidean domain, and $A$ a $m\times n$ matrix. I want to prove two things:

1) The torsion submodules of $\mathrm{Coker}\;A$ and $\mathrm{Coker}\;A^T$ are isomorphic.

2) $\mathrm{Coker}\;A$ and $\mathrm{Coker}\;A^T$ are isomorphic is and only if $n=m$.

share|improve this question

1 Answer 1

Up to multiplying on the left and right by invertible square matrices, you can assume that $A$ is diagonal—a keyword to find this is «Smith normal form». With that hypothesis, your two things are easy.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.