  For a non-commutative ring R, we consider factorizations of polynomials in
R[t] where t is a central variable. A pseudo-root of a polynomial p(t) is an
element x in R, for which there exist polynomials q(t) and s(t) such that
p(t)=q(t)(t-x)s(t). We investigate the rational relationships that hold among
the pseudo-roots of p(t) by using the diamond operations for cover graphs of
modular lattices.
