2007/12/09 by Rong Luo, Luo, Rong, Zhaoyong Huang +1
Mathematics · #13D07 #16E30 #16G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #math.RT #msc:13D07 #msc:16E30 #msc:16G10
paper · pdf · doi:10.48550/arxiv.0712.1328
10 pages
arxiv created 2007/12/09 · openalex publication_date 2007/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \rm Ext1Λ(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) \rm ExtiΛ(M,Λ)=0 for i=1,2,3; and (2) \rm ExtiΛ(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.