Talk:Ring of integers

Explicit formula desired
The section Quadratic extensions reads as follows:

"If $$d$$ is a square-free integer and $$K = \mathbb{Q}(\sqrt{d})$$ is the corresponding quadratic field, then $$\mathcal{O}_K$$ 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 $d ≡ 2, 3 (mod 4)$. This can be found by computing the minimal polynomial of an arbitrary element $$a + b\sqrt{d} \in \mathbf{Q}(\sqrt{d})$$ where $$a,b \in \mathbf{Z}$$."

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)

"Number ring"
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)