Totally real number field
id:
totally-real-number-field-261-4112598
title:
Totally real number field
text:
In number theory, a number field F is called totally real if for each embedding of F into the complex numbers the image lies inside the real numbers. Equivalent conditions are that F is generated over Q by one root of an integer polynomial P, all of the roots of P being real; or that the tensor product algebra of F with the real field, over Q, is isomorphic to a tensor power of R. For example, quadratic fields F of degree 2 over Q are either real, or complex, depending on whether the square root
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Totally_real_number_field
date created:
date modified:
2021-12-10T12:56:45Z
main entity:
{"identifier":"Q2997826","url":"https://www.wikidata.org/entity/Q2997826"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/0/06/TotallyReal.svg","width":582,"height":582}
fields total:
13
integrity:
14