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nLab: Algebraic Number
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Concise nLab wiki entry defining algebraic numbers as roots of polynomials with rational coefficients, with links to algebraic integers, number fields and algebraic closure. Terse and category-theoretic in style, so it suits readers who already know abstract algebra.
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Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
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Algebraic Number Theory
Learn algebraic number theory with Prof. Benedict Gross! Explore algebraic numbers and their properties in this comprehensive course.