When are torsionless modules projective
When are torsionless modules projective
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DOI：
10.1016/j.jalgebra.2008.04.027
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发表时间：
2007-12
影响因子：
0.9
通讯作者：
R. Luo;Zhaoyong Huang
中科院分区：
文献类型：
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作者：
R. Luo;Zhaoyong Huang
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 ExtΛ1(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) ExtΛi(M,Λ)=0 for i=1,2,3; and (2) ExtΛi(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.
