… ) in terms of homological dimensions of certain finitely generated modules. Our argument has
… For example, we establish that R is Gorenstein if the Gorenstein injective dimension of the …

… A new homological dimension, called rigidity dimension, is … dimensional algebras (especially
of infinite global dimension) … in this article is a new homological dimension, which provides …

… While there is currently no satisfactory theory of characteristic varieties for coadmissible
ÙD-modules, we can adopt the homological viewpoint by slightly generalizing the dimension …

… Tameness and its homological theory are new even in the … In the context of persistent homology
of filtered topological spaces, … structures in terms of birth and death of homology classes. …

… We show that rigid locally free H-modules are up to isomorphism determined by their rank
vectors. The same section includes the proof of the vertical bijection in Theorem 1.1. We also …

… \)-rigid modules over … rigid modules are the algebras of radical square zero (see [2]), but
this class is not large enough for our purposes. In this section we study the \(\tau \)-rigid modules …

… -Macaulay), can be used as test modules, which detect finite homological dimensions of …
modules. We show that every Ulrich module of dimension s over a local ring is (s+1)-Tor-rigid-…

… dimension at most one in terms of τ-rigid modules. We show that every indecomposable
module over iterated tilted algebras of Dynkin type is τrigid. … on homological dimension which is …

… projective and injective dimensions of a finite module M over … of the finiteness of certain
homological dimensions of M if R is … module N over a local ring (R,m,k) is said to be strongly rigid …

… new homological dimension is introduced to measure the quality of resolutions of ‘singular’
finite dimensional algebras (of infinite global dimension… a new homological dimension, which …