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Samuel Hambleton
Samuel Hambleton
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Let $K$ be a number field of degree $n$ over the rationals. Under what conditions does there exist a non-rational algebraic integer $\alpha $ in $K$ such that the discriminant of $\alpha $ divides the norm of $\alpha$?

This question was first asked on Math StackExchange, Question 29238492923849, two weeks ago.

Let $K$ be a number field of degree $n$ over the rationals. Under what conditions does there exist a non-rational algebraic integer $\alpha $ in $K$ such that the discriminant of $\alpha $ divides the norm of $\alpha$?

This question was first asked on Math StackExchange, Question 2923849, two weeks ago.

Let $K$ be a number field of degree $n$ over the rationals. Under what conditions does there exist a non-rational algebraic integer $\alpha $ in $K$ such that the discriminant of $\alpha $ divides the norm of $\alpha$?

This question was first asked on Math StackExchange, Question 2923849, two weeks ago.

Source Link
Samuel Hambleton
Samuel Hambleton
  • 655
  • 5
  • 10

Does there always exist a non-rational algebraic integer in a number field whose discriminant divides its norm?

Let $K$ be a number field of degree $n$ over the rationals. Under what conditions does there exist a non-rational algebraic integer $\alpha $ in $K$ such that the discriminant of $\alpha $ divides the norm of $\alpha$?

This question was first asked on Math StackExchange, Question 2923849, two weeks ago.