## Associative Algebra

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.''

Finch, S. Zero Structures in Real Algebras.'' http://www.mathsoft.com/asolve/zerodiv/zerodiv.html.