… ) 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 …

… It follows from the definition that rigid-test modules are strongly-rigid, but we … -rigid modules.
However, to obtain the conclusion of Theorem 1.1(i) when n ≥ depth(N), we need Tor-rigidity…

… 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 …

… ; it says that in the situation of the rigidity theorem, the class a\ acts … Section 4 contains the
proof of the rigidity theorem, which is a … an epimorphism in integral homology in dimension 2. …

… 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. …

… study these modules in relation to complexes of injective modules with complete homology,
… a big Cohen-Macaulay module and a complete module of finite injective dimension, that ring …

… 1-orthogonal modules, which play a role in the higher dimensional Auslander–Reiten …
maximal rigid Λ-modules. More precisely we define a mutation operation on maximal rigid modules…

… rigidity theorem for hypersurfaces, in which nei ther of the modules is assumed to be finite
projective dimension… statement to a statement concerning Koszul homology. We begin with two …

… results for the homological dimensions: flat dimension, injective dimension, CI-dimension,
and Gdimension; in the second we discuss a related asymptotic homological condition. We …