# Associativity

From Encyclopedia of Mathematics

*law of associativity*

A property of an algebraic operation. For the addition and multiplication of numbers associativity is expressed by the following identities:

A binary algebraic operation * is associative (or, which is the same thing, satisfies the law of associativity) if the identity

is valid in the given algebraic system. In a similar manner, associativity of an -ary operation is defined by the identities

for all .

**How to Cite This Entry:**

Associativity.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Associativity&oldid=17122

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