On subdirect factors of a projective module and applications to system theory. (English) Zbl 1352.16003
Summary: We extend a result of D. N. Avelli and P. Rocha [Syst. Control Lett. 59, No. 3–4, 203–208 (2010; Zbl 1223.93020)] 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 \(P\cong M\times_TN\) over a factor module \(T\) of grade at least 2 then the torsion-free factor of \(M\) (resp. \(N\)) is projective.
MSC:
| 16D40 | Free, projective, and flat modules and ideals in associative algebras |
| 93A10 | General systems |
| 93B25 | Algebraic methods |
Keywords:
subdirect products; finitely generated projective modules; torsion-free factors; system theoryCitations:
Zbl 1223.93020References:
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