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 $(1, (1 + \sqrt d)/2)$ if $d \equiv 1 (mod 4)$ and by $(1, \sqrt d)$ if $d \equiv 2, 3 (mod 4)$ .^[1] 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)[reply]

"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)[reply]

^ Samuel 1972, p. 35.

[FOOTNOTESamuel197235-1] Samuel 1972, p. 35.

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