In this survey article we describe some geometric results in the theory of noncommutative
rings and, more generally, in the theory of abelian categories. Roughly speaking and by …

This paper is motivated by the question whether there is a nice structure theory of finitely
generated modules over the Iwasawa algebra, ie the completed group algebra, Λ of ap-adic …

A ring with an Auslander dualizing complex is a generalization of an Auslander–Gorenstein
ring. We show that many results which hold for Auslander–Gorenstein rings also hold in the …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a
noncommutative analogue of projective 3-space. The degree-two component of the algebra …

We generalize the theory of local cohomology and local duality to a large class of non-
commutative N‐graded noetherian algebras; specifically, to any algebra, B, that can be …

In this paper, we define a notion of noncommutative graded isolated singularity, and study
AS-Gorenstein isolated singularities and the categories of graded maximal Cohen …

Connected Graded Gorenstein Algebras with Enough Normal Elements Page 1 Ž . JOURNAL
OF ALGEBRA 189, 390405 1997 ARTICLE NO. JA966885 Connected Graded Gorenstein …

Let k be a field and A be a noetherian graded algebra finitely generated in degree 1 over k.
There are two basic ingredients to study A in noncommutative algebraic geometry, namely …

In this paper, the new techniques and results concerning the structure theory of modules
over noncommutative Iwasawa algebras are applied to arithmetic: we study Iwasawa …