In simple terms, let , , and be members of an Algebra. Then the Algebra is said to be associative
where denotes Multiplication. More formally, let denote an -algebra, so that is a
Vector Space over and
Then is said to be -associative if there exists an -D Subspace of such that
for all and . Here, Vector Multiplication is assumed to be Bilinear.
An -D -associative Algebra is simply said to be ``associative.''
See also Associative
Finch, S. ``Zero Structures in Real Algebras.''
© 1996-9 Eric W. Weisstein