Philosophy of contraherent cosheaves

L Positselski - arXiv preprint arXiv:2311.14179, 2023 - arxiv.org
… of very flat modules [61, 85], as well as our work on a related topic of strongly flat and quite
flat … with an exact forgetful functor C–comod −→ R–mod if and only if C is a flat R-module. The …

A UNIFIED APPROACH TO VARIOUS GORENSTEIN MODULES

R Zhao, Y Li - Rocky Mountain Journal of Mathematics, 2022 - projecteuclid.org
… According to [27], an R-module M is said to be FP-injective (or absolutely pure [20]) if Ext1
… So applying the functor C ⊗R − to the exact sequence (4-3), we obtain the exact sequence …

Gillespie's questions and Grothendieck duality

J Wang, Z Liu, G Yang - Comptes Rendus. Mathématique, 2021 - numdam.org
… right coherent rings such that all flat left modules have finite … with compact support” functor
between derived categories of … (M,D) = 0 for all Ding injective modules D and all FP-injective

An explicit self-dual construction of complete cotorsion pairs in the relative context

L Positselski - Rendiconti Semin. Matem. Univ. Padova, 2023 - ems.press
… in the so-called strongly flat cotorsion pairs, and sometimes also in the flat cotorsion pair,
were … C, our exact sequence remains exact after applying the functor HomR.A;/. The resulting …

D4-objects in abelian categories: Transfer via functors

D Keskin Tütüncü, B Kalebogaz - Communications in Algebra, 2022 - Taylor & Francis
… and Olteanu investigated transfers of strongly Rickart objects in … this statement when L
is a faithful functor (see Theorem 2.17). … Let F denote the full subcategory of all flat right S-modules, …

Cotilting sheaves over weighted noncommutative regular projective curves

D Kussin, R Laking - Documenta Mathematica, 2020 - content.staging.ems.press
… and of indecomposable pureinjective objects are strongly related to each other. In this paper
… We will denote the category of additive functors from T c to Ab by T c-Mod. Since T is k-linear…

The finitistic dimension conjecture via DG-rings

L Shaul - arXiv preprint arXiv:2209.02068, 2022 - arxiv.org
… one is able to obtain strong results about the finitistic dimension… Finally, we require the next
result that relies heavily on our … By a repeated use of stupid truncation functors, we may find a …

How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

Y Ma, J Lü, H Li, J Hu - Journal of Algebra and Its Applications, 2023 - World Scientific
… Firstly, we introduce the following functors which are defined in [9]. … 1], where Flat(R)
denotes the class of flat left R-modules and FP-Inj(Rop) denotes the class of FP-injective right R-…

[HTML][HTML] Recollements from cotorsion pairs

S Bazzoni, M Tarantino - Journal of Pure and Applied Algebra, 2019 - Elsevier
… of the homotopy category of flat modules and he obtained a … Our results are strongly based
on the two papers [20] and [19… FpInj denotes the class of Fp-injective modules, that is the right …

On nonnil-pure theories

YE Haddaoui, H Kim, N Mahdou - Beiträge zur Algebra und Geometrie …, 2024 - Springer
… that if R is a strongly \(\phi \)-ring, then R/I is never \(\phi \)-flat for any proper nonnil ideal I of
R. … R-module is nonnil-FP-injective, we argue that every R-module is \(\phi \)-flat. For any R-…