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Is the set $\mathbb{Q}$ under $×$ an abelian group? It is sure for $\mathbb{Q} - {0}$, but i think the whole set of rationals is not an abelian group as $0 × a = a × 0 = 0$, but the identity element is $1$ and i think it must be unique, and $a$ is not equal to $0$. Can you please help me whether it is an abelian group under $×$ or not?

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It is not a group under multiplication, since $0$ has no inverse.

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  • $\begingroup$ Sir i have requested for deletion of my account so i restored everything. Will the question be still there after my account is delete? $\endgroup$ – user655794 Mar 25 at 19:15

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