  We call a graded connected algebra $R$ effectively coherent, if for every
linear equation over $R$ with homogeneous coefficients of degrees at most $d$,
the degrees of generators of its module of solutions are bounded by some
function $D(d)$. For commutative polynomial rings, this property has been
established by Hermann in 1926. We establish the same property for several
classes of noncommutative algebras, including the most common class of rings in
noncommutative projective geometry, that is, strongly Noetherian rings, which
includes Noetherian PI algebras and Sklyanin algebras.
  We extensively study so--called universally coherent algebras, that is, such
that the function $D(d)$ is bounded by 2d for $d >> 0$. For example, finitely
presented monomial algebras belong to this class, as well as many algebras with
finite Groebner basis of relations.
