Let R be a commutative Noetherian local ring and M, N be finitely generated R-modules. We
prove a number of results of the form: if Hom R (M, N) has some nice properties and Ext R …

We study homological properties of test modules that are, in principle, modules that detect
finite homological dimensions. The main outcome of our results is a generalization of a …

We study two properties for a pair of finitely generated modules over a local hypersurface $
R $: decency, which is close to proper intersection of the supports, and $\operatorname {Tor} …

Given finitely generated modules M and N over a local ring R, the tensor product M⊗ RN
typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

In this paper we describe inductive machinery to investigate asymptotic behavior of
homology groups and related invariants of representations of certain graded combinatorial …

We survey some recent developments in understanding homological properties of finitely
generated modules over a complete intersection. These properties mainly concern with …

In this paper we study a long-standing conjecture of Huneke and Wiegand which is
concerned with the torsion submodule of certain tensor products of modules over one …

Let R be a local complete intersection ring and let M and N be nonzero finitely generated R-
modules. We employ Auslander's transpose in the study of the vanishing of Tor and obtain …

In this paper we study rigid modules over commutative Noetherian local rings, establish new
freeness criteria for certain periodic rigid modules, and extend several results from the …