Difference between revisions of "Commutativity"
From Encyclopedia of Mathematics
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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 | ||
| − | + | \begin{equation} | |
| − | + | a+b=b+a,\quad \text{ and } \quad ab=ba. | |
| − | + | \end{equation} | |
| − | A binary operation | + | 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=17315
Commutativity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Commutativity&oldid=17315
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article