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Difference between revisions of "Commutativity"

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A property of algebraic operations (cf. [[Algebraic operation|Algebraic operation]]). For addition and multiplication, commutativity is expressed by the formulas
 
A property of algebraic operations (cf. [[Algebraic operation|Algebraic operation]]). For addition and multiplication, commutativity is expressed by the formulas
 
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\begin{equation}
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023420/c0234201.png" /></td> </tr></table>
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a+b=b+a,\quad \text{ and } \quad ab=ba.
 
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\end{equation}
A binary operation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023420/c0234202.png" /> is commutative (or, what is the same, satisfies the law of commutativity) if in the given algebraic system the identity <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c023/c023420/c0234203.png" /> holds
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A binary operation $*$ is commutative (or, what is the same, satisfies the law of commutativity) if in the given algebraic system the identity $a*b=b*a$ holds

Revision as of 06:21, 14 December 2012


A property of algebraic operations (cf. Algebraic operation). For addition and multiplication, commutativity is expressed by the formulas \begin{equation} a+b=b+a,\quad \text{ and } \quad ab=ba. \end{equation} A binary operation $*$ is commutative (or, what is the same, satisfies the law of commutativity) if in the given algebraic system the identity $a*b=b*a$ holds

How to Cite This Entry:
Commutativity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Commutativity&oldid=29183
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article