What is the integral closure of the ring $\mathbb{Z}$ inside the field $\mathbb{R}$ of real numbers and what are it's properties? Is this studied at all?
2025-01-13 09:52:30.1736761950
What is the integral closure of the integers in the real numbers?
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The real algebraic integers; that is, the intersection of $\mathbb{R}$ and the algebraic integers in $\mathbb{C}$. It's generally more profitable to study all algebraic integers since, for example, the Galois conjugates of a real algebraic integer need not be real.