There's a question that says, "Prove that the ring of integers O in the quadratic integer ring Q$\displaystyle \sqrt{2}$ is a Euclidean Domain.

What do they mean by ring of integers O?

I know Q$\displaystyle \sqrt{2}$={q + r$\displaystyle \sqrt{2}$;q,r in Q}

... so would the ring of integers be O = {q + 0$\displaystyle \sqrt{2}$;q in Z} or do they mean algebraic integers or something?