2009/06/06 by Huang, Chonghui, Huang, Zhaoyong · 1 citation
#16E05 #16E10 #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0906.1253
Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n≥ 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated left (or right) R-module has Gorenstein dimension at most n. For any n ≥ 1, we study the properties of the finitely generated R-modules M with \ExtRi(M, R)=0 for any 1≤ i ≤ n. Then we investigate the relation between these properties and the self-injective dimension of R.