## Zero Divisor

A Nonzero element of a Ring for which , where is some other Nonzero element and the vector multiplication is assumed to be Bilinear. A Ring with no zero divisors is known as an Integral Domain. Let denote an -algebra, so that is a Vector Space over and

Now define

where . is said to be -Associative if there exists an -dimensional Subspace of such that for all and . is said to be Tame if is a finite union of Subspaces of .

References

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

© 1996-9 Eric W. Weisstein
1999-05-26