mersenneforum.org - View Single Post - Factorization of Ideals in Number Field, Looking for Reference

Nick · 2013-01-02, 09:44

Quote:

Originally Posted by jinydu

Thanks. I presume 'rational integer' and 'rational prime' mean 'element of $\mathbb{Q}$ ' and 'prime in $\mathbb{Q}$ ' respectively? As opposed to 'element of $\mathbb{O_K}$ ' and 'prime in $\mathbb{O_K}$ '?

Yes (but with $\mathbb{Z}$ instead of $\mathbb{Q}$ ):
in algebraic number theory, the elements of $\mathbb{Z}$ are called rational integers to distinguish them from algebraic integers, and similarly with primes.