Difference between revisions of "Non-Abelian number field"
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| − | An algebraic [[ | + | An algebraic [[number field]] with a non-Abelian [[Galois group]] over the field of rational numbers $\QQ$, |
| − | or a field that is not normal over $ | + | or a field that is not normal over $ \QQ$. |
| − | Sometimes, instead of | + | Sometimes, instead of $\QQ$, one considers some other ground field $k$ |
| − | one considers some other ground field | + | of algebraic numbers, and the term "non-Abelian" is understood to refer to the Galois group over $k$. |
| − | of algebraic numbers, and the term "non-Abelian" is understood to refer to the Galois group over | ||
| − | |||
| − | |||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9</TD></TR> | ||
| + | </table> | ||
Latest revision as of 15:13, 10 April 2023
An algebraic number field with a non-Abelian Galois group over the field of rational numbers $\QQ$,
or a field that is not normal over $ \QQ$.
Sometimes, instead of $\QQ$, one considers some other ground field $k$
of algebraic numbers, and the term "non-Abelian" is understood to refer to the Galois group over $k$.
References
| [a1] | E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9 |
How to Cite This Entry:
Non-Abelian number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-Abelian_number_field&oldid=47981
Non-Abelian number field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-Abelian_number_field&oldid=47981
This article was adapted from an original article by L.V. Kuz'min (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article