Related papers: Infinite dimensional excellent rings
We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.
The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.
We provide the spherical systems of the wonderful reductive subgroups of any reductive group.
We extend the notion of type sequence to rings that are not necessarily residually rational. Using this invariant we characterize different types of rings as almost Gorenstein rings and rings of maximal length.
There are Noetherian rings (in fact domains) with a free additive group, in every infinite cardinality. (This is an expanded version of [SgSh:217] which appears in the Abstracts of the American Mathematical Society 7 (1986): 369.)
We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces,…
We discuss projective equivalence of ideals in Noetherian rings and the existence or failure of existence of projectively full ideals. We describe connections with the Rees valuations and Rees integers of an ideal, and consider the question…
The first examples of exceptional terminal singularities are constructed.
This paper proves finite generation of the log canonical ring without Mori theory.
In this note, we define and investigate ideal covering numbers of associative rings (not assumed to be commutative or unital): three invariants defined as the minimal number of proper left, right, or two-sided ideals whose union equals the…
We give a sufficient condition on totally disconnected topological graphs such that their associated topological graph algebras are purely infinite.
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We investigate Diophantine definability and decidability over some subrings of algebraic numbers contained in quadratic extensions of totally real algebraic extensions of $\mathbb Q$. Among other results we prove the following. The big…
We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…
We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of positive radius, some point exists in $X$ which belongs to infinitely many balls.
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.
In this paper, we prove the infinite dimensionality of some local and global cohomology groups on abstract Cauchy-Riemann manifolds.
There has arisen in recent years a substantial theory of "multiplier ideals'' in commutative rings. These are integrally closed ideals with properties that lend themselves to highly interesting applications. But how special are they among…
A ring with a test module of finite upper complete intersection dimension is complete intersection.
We show the Graceful Tree Conjecture holds.