Questions related to the algebraic structure of algebraic integers

learn more… | top users | synonyms

22
votes
0answers
163 views
+100

Does every ring of integers sit inside a ring of integers that has a power basis?

Given a finite extension of the rationals, K, we know that $K=\mathbb{Q}[\alpha]$ by the primitive element theorem, so every $x \in K$ has the form $$x = a_0 + a_1 \alpha + ... + a_n \alpha^n$$ with ...