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'anti-isomorphism'
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| Title of object: |
anti-isomorphism |
| Canonical Name: |
AntiIsomorphism |
| Type: |
Definition |
| Created on: |
2006-06-17 23:09:39 |
| Modified on: |
2006-06-17 23:09:39 |
| Classification: |
msc:16B99, msc:13B10 |
| Defines: |
anti-endomorphism |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
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%\usepackage{amsthm}
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%\usepackage{xypic}
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Content:
A function $f: R->S$ is said to be an ${\it anti-isomorphism}$ if it is an
isomorphism of the additive groups of $R$ and $S$ and
$f(r_{1}r_{2}) = f(r_{2}r_{1})$ for all $r_{1}, r_{2} \in R$.
If $R=S$, then $f$ is called an ${\it anti-endomorphism}$.
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