Related papers: Finiteness conditions and cotorsion pairs

We investigate Tate cohomology of modules over a commutative noetherian ring with respect to semidualizing modules. We identify classes of modules admitting Tate resolutions and analyze the interaction between the corresponding relative and…

In this work we study a kind of coherence condition on FI_G-modules, which generalizes the usual notion of finite generation. We prove that a module is coherent, in the appropriate sense, if and only if its generators, as well as its…

In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings…

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the classes $ \mathcal{P}_C $ and $ \mathcal{I}_C $, we extend the notions of perfect and coperfect modules introduced by D.Rees \cite{R} and…

Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the projective and injective dimensions of a finite module $M$ over a (commutative) Noetherian ring $R$. Second, in the other direction, we…

Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (e.g., structured ring spectra). We prove…

Let $\fa$ be an ideal of a local ring $(R,\fm)$ and $M$ a finitely generated $R$-module. We investigate the structure of the formal local cohomology modules ${\vpl}_nH^i_{\fm}(M/\fa^n M)$, $i\geq 0$. We prove several results concerning…

We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a not-necessarily commutative ring $R$ that coincides with the $R$-topology defined by Matlis when $R$ is commutative. (2) We…

We show that any homomorphism between Noetherian $F$-finite rings can be factored into a regular morphism between Noetherian $F$-finite rings followed by a surjection. This result establishes an analog of the 'smooth-by-surjective'…

We introduce a criterion for the completeness of ring approximations of modular cohomology rings of finite non prime power groups, and discuss how this criterion performs in practical computations, compared with other criteria.

We describe new classes of noetherian local rings $R$ whose finitely generated modules $M$ have the property that $Tor_i^R(M,M)=0$ for $i\gg 0$ implies that $M$ has finite projective dimension, or $Ext^i_R(M,M)=0$ for $i\gg 0$ implies that…

Recentely, Anderson and Dumitrescu's $S$-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of $S$-finitely presented modules and then of $S$-coherent rings which are $S$-versions of finitely…

We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case…

We prove coherence of relatively quasi-free algebras over noetherian rings. Chase criterion for coherence is used.

Very flat and contradjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian…

Let R be a ring, X a class of R-modules and n>1 an integer. In this paper, via special finitely presented modules, we introduce the concepts of Gorenstein n-X-injective and n-X-flat modules. And aside, we obtain some equivalent properties…

For a commutative noetherian ring $R$, we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of…

We show that if a class of modules is closed under pure quotients, then it is precovering if and only if it is covering, and this happens if and only if it is closed under direct sums. This is inspired by a dual result by Rada and…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $\widehat{R}$ its $\mathfrak{m}$-adic completion. We study the problem of determining when a finitely generated $\widehat{R}$-module arises from an $R$-module, i.e., when it is…

To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants…