ar X iv : 0 71 2 . 13 28 v 1 [ m at h . R A ] 9 D ec 2 00 7 When Are Torsionless Modules Projective ?
نویسنده
چکیده
In this paper, we study the problem when a finitely generated torsionless module is projective. Let Λ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless Λ-module M is projective if Ext Λ (M,M) = 0. For a commutative Artinian ring Λ, a finitely generated torsionless Λ-module M is projective if the following conditions are satisfied: (1) Ext Λ (M,Λ) = 0 for i = 1, 2, 3; and (2) Ext Λ (M,M) = 0 for i = 1, 2. As a consequence of this result, we have that for a commutative Artinian ring Λ, a finitely generated Gorenstein projective Λ-module is projective if and only if it is selforthogonal.
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