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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:
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