Definition:Divisor-Finite Monoid

Definition
Let $(M, *)$ be a monoid.

Then $M$ is divisor-finite for all $m \in M$ the set:
 * $\{(x, y) \in M^2 : x*y = m \}$

is finite.

Also see

 * Definition:Convolution of Mappings on Divisor-Finite Monoid
 * Definition:Big Monoid Ring