For a left and right Noetherian ring $R$, we give some equivalent characterizations for $\_RR$ satisfying the Auslander condition in terms of flat (resp. injective) dimensions minimal injective coresolution resolution) $R$-modules. Furthermore, prove that an artin algebra $R$ condition, is Gorenstein if only subcategory consisting finitely generated modules contravariantly finite. As applicatio...

We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension n ≥ 4 through the theory of Hilbert scheme of group orbits.

We present and study the concept of m-periodic Gorenstein objects relative to a pair (A,B) classes in an abelian category, as generalization m-strongly projective modules over associative rings. prove several properties when satisfies certain homological conditions, like for instance is GP-admissible pair. Connections dimensions these pairs are also established.

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.