What Does I' Represent in Zsqrt(d)?

[mgsumsums]

Homework Statement

Show I' ideal in Zsqrt(d)
Let I'=I intersection Z (where Z denotes the integers)
I any ideal in Zsqrt(d)

Homework Equations

The Attempt at a Solution

I think I' is just the set of integers in Z such that the integer is an ideal of zsqrt(d)
But how is this ideal since if I left or right multiply any element of zsqrt(d) with an element in I' I get an elementary with an imaginary component?

 

[mgsumsums]

Problem solved prof made a typo sorry