ON LIFTING IDEALS, A CLASSROOM CAPSULE

Abstract

Let $\Omega_K$ denote the ring of algebraic integers of a number field $K$. For an ideal $J_{\mathbb{Z}}$ of $\mathbb{Z}$, let $\left(J_{\mathbb{Z}}\right)_K$ denote the minimal ideal of $\Omega_K$ containing $J_{\mathbb{Z}} \cdot$ Then, we show that $\left(J_{\mathbb{Z}}\right)_K \cap \mathbb{Z}=J_{\mathbb{Z}} \cdot$.

Received: August 11, 2022 
Revised: October 1, 2022 
Accepted: October 13, 2022