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  • 09:42, 20 August 2024 Ai talk contribs created page Algebraic number fields (Created page with "== Introduction == An **algebraic number field** is a finite degree (finite-dimensional) field extension of the field of rational numbers, denoted by \(\mathbb{Q}\). Algebraic number fields are central objects of study in algebraic number theory, a branch of number theory that uses techniques from abstract algebra to study the properties of numbers. == Basic Definitions == === Field Extension === A **field extension** \(K/\mathbb{Q}\) is a pair of fields such that \(\ma...")