# Difference between revisions of "Commutativity"

From Encyclopedia of Mathematics

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− | A property of algebraic operations (cf. [[ | + | A property of algebraic operations (cf. [[Algebraic operation]]). For addition and multiplication, commutativity is expressed by the formulas |

\begin{equation} | \begin{equation} | ||

a+b=b+a,\quad \text{ and } \quad ab=ba. | a+b=b+a,\quad \text{ and } \quad ab=ba. | ||

\end{equation} | \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 | + | 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. |

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+ | [[Category:General algebraic systems]] |

## Latest revision as of 22:17, 26 October 2014

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