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.

I want to study the structure of cokernel of abelian group homomorphism.

Is it true that $\mathbb{Z}^2/<(1,1)>$ is cyclic group isomorphic to $\mathbb{Z}$?

share|improve this question

1 Answer 1

Let $\varphi\colon\mathbb Z^2\to \mathbb Z$, $\varphi(x,y)=x-y$. Then $\varphi$ is a homomorphism. Since $\ker\varphi = \langle (1,1)\rangle$ and $\varphi$ is surjective, the first isomorphism theorem gives the answer.

share|improve this answer

Your Answer


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.