Is $\displaystyle \{bi: b \in \mathbb{Z}\}$ where $\displaystyle i^2=-1$ a ring?

I am assuming it isnt since (bi)*(ci)=-bc where b and c are elements of Z

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- Aug 18th 2012, 08:23 PMmathrldRing
Is $\displaystyle \{bi: b \in \mathbb{Z}\}$ where $\displaystyle i^2=-1$ a ring?

I am assuming it isnt since (bi)*(ci)=-bc where b and c are elements of Z - Aug 18th 2012, 08:35 PMDevenoRe: Ring
that is correct, the set is not closed under multiplication.

- Aug 18th 2012, 08:52 PMmathrldRe: Ring
Thanks :)))))