Perfect field
id:
perfect-field-188-10275826
title:
Perfect field
text:
In algebra, a field k is perfect if any one of the following equivalent conditions holds:
- Every irreducible polynomial over k has no multiple roots in any field extension F/k.
- Every irreducible polynomial over k has non-zero formal derivative.
- Every irreducible polynomial over k is separable.
- Every finite extension of k is separable.
- Every algebraic extension of k is separable.
- Either k has characteristic 0, or, when k has characteristic p > 0, every element of k is a pth
brand slug:
wiki
category slug:
encyclopedia
description:
Algebraic structure
original url:
https://en.wikipedia.org/wiki/Perfect_field
date created:
2004-03-04T21:23:34Z
date modified:
2024-09-08T22:15:35Z
main entity:
{"identifier":"Q2997817","url":"https://www.wikidata.org/entity/Q2997817"}
image:
fields total:
13
integrity:
15