In simple terms, let , , and be members of an Algebra. Then the Algebra is said to be associative
if

(1) 
where denotes Multiplication. More formally, let denote an algebra, so that is a
Vector Space over and

(2) 

(3) 
Then is said to be associative if there exists an D Subspace of such that

(4) 
for all and . Here, Vector Multiplication is assumed to be Bilinear.
An D associative Algebra is simply said to be ``associative.''
See also Associative
References
Finch, S. ``Zero Structures in Real Algebras.''
http://www.mathsoft.com/asolve/zerodiv/zerodiv.html.
© 19969 Eric W. Weisstein
19990525