What Does I' Represent in Zsqrt(d)?

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SUMMARY

The discussion centers on the ideal I' in the ring Z√d, specifically addressing the intersection of an ideal I with the integers Z. It concludes that I' consists of integers that form an ideal within Z, despite initial confusion regarding the multiplication of elements from Z√d with those in I'. The participant ultimately resolves the issue by identifying a potential typo in the professor's statement.

PREREQUISITES
  • Understanding of ring theory and ideals
  • Familiarity with the structure of Z√d (the ring of integers adjoined with √d)
  • Knowledge of integer properties and operations
  • Basic concepts of algebraic number theory
NEXT STEPS
  • Study the properties of ideals in algebraic number fields
  • Explore the concept of intersections of ideals in ring theory
  • Learn about the structure and properties of Z√d
  • Investigate common typos and misconceptions in mathematical proofs
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Students of algebra, mathematicians focusing on number theory, and anyone studying the properties of ideals in algebraic structures.

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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?

 
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Problem solved prof made a typo sorry
 

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