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'finite extension'
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| Title of object: |
finite extension |
| Canonical Name: |
FiniteExtension |
| Type: |
Definition |
| Created on: |
2001-11-08 01:28:04-05 |
| Modified on: |
2002-05-26 02:04:03-04 |
| Classification: |
msc:12F05 |
| Keywords: |
Galois Theory, Field |
Revision comment (for changes between this and next version):
| Changes for correction #1410 ('synonym'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
Let $K$ an extension field of $F$. We say that $K$ is a \emph{finite extension} if
$[K:F]$ is finite. That is, $K$ is a finite dimensional space over $F$.
An important result on finte extensions establishes that any finite extension is also an algebraic extension. |
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