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
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