We define and study a notion of Gorenstein projective dimension for complexes of left
modules over associative rings. For complexes of finite Gorenstein projective dimension we …

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

For finite modules over a local ring the general problem is considered of finding an
extension of the class of modules of finite projective dimension preserving various …

We discuss vanishing of cohomology of finite modules over Cohen-Macaulay local rings
$(R,\mathfrak m) $. Special attention is given to the case when the modules are annihilated …

Let (R, m) be a commutative Noetherian local ring with m 3=(0). We give a condition for R to
have a non-free module of G-dimension zero. We shall also construct a family of non …

We show that the set S (R) of shift-isomorphism classes of semidualizing complexes over a
local ring R admits a nontrivial metric. We investigate the interplay between the metric and …

We extend the notions of complete intersection dimension and lower complete intersection
dimension to the category of complexes with finite homology and verify basic properties …

Let $ R $ be a commutative noetherian local ring of prime characteristic. Denote by ${{}^
e\hspace {-1.6 pt}{}} R $ the ring $ R $ regarded as an $ R $-algebra through $ e $-times …

Following the well‐established terminology in commutative algebra, any (not necessarily
commutative) finite‐dimensional local algebra AA with radical JJ will be said to be short …

This paper studies infinite acyclic complexes of finitely generated free modules over a
commutative noetherian local ring $(R,\fm) $ with $\fm^ 3= 0$. Conclusive results are …