When Are Torsionless Modules Projective?
| dc.creator | Luo, Rong | |
| dc.creator | Huang, Zhaoyong | |
| dc.date | 2007-12-09 | |
| dc.date.accessioned | 2026-07-07T08:48:10Z | |
| dc.date.available | 2026-07-07T08:48:10Z | |
| dc.description | 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 ${\rm Ext^1_Λ}(M,M)=0$. For a commutative Artinian ring $Λ$, a finitely generated torsionless $Λ$-module $M$ is projective if the following conditions are satisfied: (1) ${\rm Ext}^i_Λ(M,Λ)=0$ for $i=1,2,3$; and (2) ${\rm Ext}^i_Λ(M,M)=0$ 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. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0712.1328 | |
| dc.identifier | http://arxiv.org/abs/0712.1328 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143853 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.subject | 16E30; 13D07; 16G10 | |
| dc.title | When Are Torsionless Modules Projective? | |
| dc.type | text |