How many additive cosets exist for the ideal I in the subring R?

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The discussion centers on the number of additive cosets for the ideal I in the subring R, defined as R = {x + yi : x, y in 2Z} and I = {x + yi : x, y in 2Z}. The user seeks clarification on the definition of additive cosets and the relationship between the ideal and the subring. It is established that the ideal I is indeed equal to the subring R, leading to the conclusion that there is only one additive coset of I in R.

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Let R be the subring {x + yi : x, y in 2Z} of C, and
let I be the ideal {x + yi : x,y in 2Z}of R.
How many additive cosets has I in R? List them clearly.

I know definition of ideal but ı don't know how to write in set is that question describe.Please help :)
 
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Did you make a typo?? The way you wrote it implies that I=R.
 

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