Difference between revisions of "Algebraic number field"
From Encyclopedia of Mathematics
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| + | 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 theory]]; [[Extension of a field|Extension of a field]]; [[Number field]].) | ||
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| + | ====References==== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9</TD></TR> | ||
| + | </table> | ||
Revision as of 17:08, 20 December 2014
2020 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 theory; Extension of a field; Number field.)
References
| [1] | E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9 |
How to Cite This Entry:
Algebraic number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebraic_number_field&oldid=30303
Algebraic number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebraic_number_field&oldid=30303