Difference between revisions of "Algebraic number field"
From Encyclopedia of Mathematics
(Redirect to Number field for the present) |
(expand with comment from Number field article) |
||
| Line 1: | Line 1: | ||
| − | + | {{TEX|done}}{{MSC|11R04}} | |
| + | 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]].) | ||
| + | |||
| + | ====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=35749
Algebraic number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebraic_number_field&oldid=35749