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For questions on modules over rings.
4
votes
Accepted
Reference request for stably free modules
The standard term for a ring satisfying (F) (for right modules) is a (right) Hermite ring. … A good introductory treatment, including proofs of (2a) and (2b), is contained in Section I.4 of Lam's book "Serre's problem on projective modules." …
3
votes
tilting module
Just check that $T \oplus P$ is also a tilting module, and then use the fact that any two tilting $A$-modules have the same number of isomorphism classes of idecomposable summands. …