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Algebraic number field

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2010 Mathematics Subject Classification: Primary: 11R04 [MSN][ZBL]

An algebraic number field $K$ of degree $n$ is an extension of degree $n$ of the field $\mathbf Q$ of rational numbers. Alternatively, a number field $K$ is an algebraic number field (of degree $n$) if every $\alpha\in K$ is the root of a polynomial (of degree at most $n$) over $\mathbf Q$. (Cf. also Algebraic number; Algebraic number theory; Extension of a field; Number field.)

References

[1] E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9

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How to Cite This Entry:
Algebraic number field. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Algebraic_number_field&oldid=37054