Sylvester domain
In mathematics, a Sylvester domain, named after James Joseph Sylvester by ,  is a ring in which Sylvester's law of nullity holds. This means that if A is an m by n matrix, and B is an n by s matrix over R, then
ρ(AB) ≥ ρ(A) + ρ(B) – n
where ρ is the inner rank of a matrix. The inner rank of an m by n matrix is the smallest integer r such that the matrix is a product of an m by r matrix and an r by n matrix. showed that fields satisfy Sylvester's law of nullity and are, therefore, Sylvester domains. References

Ring theory