Difference between revisions of "Non-Abelian number field"
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| + | An algebraic [[Number field|number field]] with a non-Abelian [[Galois group|Galois group]] over the field of rational numbers $ \mathbf Q $, | ||
| + | or a field that is not normal over $ \mathbf Q $. | ||
| + | Sometimes, instead of $ \mathbf Q $, | ||
| + | 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 $. | ||
====Comments==== | ====Comments==== | ||
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====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> | ||
Revision as of 08:02, 6 June 2020
An algebraic number field with a non-Abelian Galois group over the field of rational numbers $ \mathbf Q $,
or a field that is not normal over $ \mathbf Q $.
Sometimes, instead of $ \mathbf Q $,
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 $.
Comments
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