We introduce a new notion of commutative noetherian local rings, which we call dominant.
We explore fundamental properties of dominant local rings and compare them with other …

We describe new classes of noetherian local rings R whose finitely generated modules M
have the property that Tor i R (M, M)= 0 for i≫ 0 implies that M has finite projective …

Let R be a commutative Noetherian local ring. We consider how nontrivial resolving/thick
subcategories of abelian/triangulated categories associated to R intersect. It is understood …