On subdirect factors of a projective module and applications to system theory
Tóm tắt
We extend a result of Napp Avelli, van der Put, and Rocha with a system-theoretic interpretation to the noncommutative case: Let
$$P$$
be a f.g. projective module over a two-sided Noetherian domain. If
$$P$$
admits a subdirect product structure of the form
$$P \cong M \times _T N$$
over a factor module
$$T$$
of grade at least
$$2$$
then the torsion-free factor of
$$M$$
(resp.
$$N$$
) is projective.