From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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:
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article