Questions related to the algebraic structure of algebraic integers

learn more… | top users | synonyms

4
votes
0answers
44 views
+50

Matrix which represents the product of ideal classes of 2 matrices.

Let $f(x)$ be an irreducible monic degree $n$ polynomial with $\mathbb{Z}$-coefficients and $\Theta$ be a root of $f(x)$. There is an old theorem of Latimer and MacDuffee that there is a 1-1 ...
5
votes
3answers
212 views
+100

Extension by adjoining roots of unity and ramification

Let $p$ be a prime, $n\geq 1$, $\zeta=\zeta_{p^n}$ a primitive $p^n$th root of unity, $L$ a number field, and $\wp$ a prime ideal of the ring of integers of $L$ lying above $p$. Suppose that ...