Related papers: On cohomological dimension and depth under linkage
We generalize some known results on the relation between the cohomological and projective dimension. Then we examine the set-theoretically Cohen-Macaulay ideals to find some cohomological characterization of these kind of ideals.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new…
We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem
In this paper we build off of Takahashi and White's $\mathcal{P}_C$-projective dimension and $\mathcal{I}_C$-injective dimension to define these dimensions for when $C$ is a semidaulizing complex. We develop the framework for these…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
Let $R$ be a commutative Noetherian ring. Using the new concept of linkage of ideals over a module, we show that if $\mathfrak{a}$ is an ideal of $R$ which is linked by the ideal $I$, then $cd(\mathfrak{a},R) \in \{ grad \mathfrak{a},…
We introduce relative preresolving subcategories and precoresolving subcategories of an abelian category and define homological dimensions and codimensions relative to these subcategories respectively. We study the properties of these…
In Enochs' relative homological dimension theory occur the so called (co)resolvent and (co)proper dimensions which are defined using proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some…
The lambda-ring cohomology in dimensions 0 and 1 of certain truncated polynomial filtered lambda-rings are computed. The dimension 1 case is related to deformations of lambda-rings.
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
In this paper we give an upper bound, in characteristic 0, for the cohomological dimension of a graded ideal in a polynomial ring such that the quotient has depth at least 3. In positive characteristic the same bound holds true by a…
Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are investigated. We focus on the asymptotic behavior of codimensions and projective dimensions of ideals in such a chain. If the ideals are graded it is…
We investigate the notion of the C-projective dimension of a module, where C is a semidualizing module. When C=R, this recovers the standard projective dimension. We show that three natural definitions of finite C-projective dimension…
Let $R$ be a commutative Noetherian ring and $M$ be a finitely generated $R$-module. Considering the new concept of linkage of ideals over a module, we study associated prime ideals, cofiniteness and Artinianness of local cohomology modules…
Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to…
Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.