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
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