Lemma 15.22.8. Let R be a Noetherian domain. Let M be a nonzero finite R-module. The following are equivalent
M is torsion free,
M is a submodule of a finite free module,
(0) is the only associated prime of M,
(0) is in the support of M and M has property (S_1), and
(0) is in the support of M and M has no embedded associated prime.
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