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Problem: Let $R=\Bbb Z(i)$ be the ring of gaussian integers

Describe the cosets of the factor ring $R$ \ $A$ where $A=Ri$.

Thoughts:The elements of $R$ \ $A$ will be of the form: $(a+bi)+Ri$. I'm not really sure how to derive some sort of equivalence classes/cosets out of this. Any insights appreciated.

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    $\begingroup$ Hint: $i$ is a unit of $R$. $\endgroup$ Feb 2, 2019 at 20:54

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Observe that $A=iR=R$ and so $R/A=\{A\}$.

Let $a+bi+A\in R/A$, then $$a+bi+A=a+bi+i(-b+ai)+A=a+bi-bi-a+A=0+A=A$$

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