Talk:Ring of integers

Latest comment: 2 years ago by Joel Brennan in topic "Number ring"

Explicit formula desired

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The section Quadratic extensions reads as follows:

"If   is a square-free integer and   is the corresponding quadratic field, then   is a ring of quadratic integers and its integral basis is given by (1, (1 + d)/2) if d ≡ 1 (mod 4) and by (1, d) if d ≡ 2, 3 (mod 4).[1] This can be found by computing the minimal polynomial of an arbitrary element   where  ."

But how about just stating what the general form of an element of the ring of algebraic integers is?

Or else, how about expressing the ring of algebraic integers as Z[α] for an explicit complex number α ?

That would be far more helpful to the reader than merely describing an "integral basis". 2601:200:C000:1A0:5D52:60BD:A6FE:A4AE (talk) 18:48, 20 June 2021 (UTC)Reply

"Number ring"

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Should the terminology "number ring" be mentioned in this article? (I don't know whether it should as I am not a number theorist) Joel Brennan (talk) 23:22, 20 April 2022 (UTC)Reply

  1. ^ Samuel 1972, p. 35.