Topological divisor of zero

In mathematics, an element "z" of a Banach algebra "A" is called a topological divisor of zero if there exists a sequence "x"1, "x"2, "x"3, ... of elements of "A" such that
If such a sequence exists, then one may assume that ||"x""n"|| = 1 for all "n".
If "A" is not commutative, then "z" is called a left topological divisor of zero, and one may define right topological divisors of zero similarly.
Generalization.
The notion of a topological divisor of zero may be generalized to any topological algebra. If the algebra in question is not first-countable, one must substitute nets for the sequences used in the definition.