In a perfect category every object has a minimal projective resolution. We give a sufficient condition for the category of modules over a category-graded algebra to be perfect. AMS Subject Classification (2000): 18E15, 16W50. In [6] the second author explored homological properties of algebras graded over a small category. Our interest in these algebras arose from our research on the homologica...

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .

We introduce notions of finite presentation and co-exactness which serve as qualitative quantitative analogues finite-dimensionality for operator modules over completely contractive Banach algebras. With these we begin the development a local theory by introducing lifting property, nuclearity, semi-discreteness. For large class prove that property is equivalent to flatness, generalizing space r...

The purpose of this paper is to prove that certain subquotients of the MF∇-objects of Faltings ([1]) are semi-positive. In particular, we obtain an algebraic proof of a result (generalizing those of [5], [9]) on the semi-positivity of the higher direct images of certain kinds of sheaves for semistable families of algebraic varieties. Our Main Theorem, proven in §3, is as follows: Theorem 3.4: L...

If H is a Hopf algebra with bijective antipode and α, β ∈ AutHopf (H), we introduce a category HYD (α, β), generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category YD(H) having all the categories HYD (α, β) as components, which ifH is finite dimensional coincides with the representations of a certain quasitriangular T-coalgebra DT (H) that we...