
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" an "n" by "s" matrix over "R", then
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.