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Order (ring theory)

In mathematics, certain subsets of some fields are called orders. The set of integers is an order in the rational numbers (the only one). In an algebraic number field ⁠ K {\displaystyle K} ⁠, an order is a ring of algebraic integers whose field of fractions is ⁠ K {\displaystyle K} ⁠, and the maximal order, often denoted ⁠ O K {\displaystyle {\mathcal…

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Algebraic number theory

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Order (ring theory)

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displaystyle order field ring number maximal integers integral algebraic subring orders mathcal -order example local rational valuation examples theory fields

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