On strongly flat and weakly cotorsion modules
Abstract
The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules with respect to a multiplicative subset or a finite collection of multiplicative subsets in a commutative ring. The strongly flat modules are characterized by a set of conditions, while the weakly cotorsion modules are produced by a generation procedure. Passing to the collection of all countable multiplicative subsets, we define quite flat and almost cotorsion modules, and show that, over a Noetherian ring with countable spectrum, all flat modules are quite flat and all almost cotorsion modules are cotorsion.
Cite
@article{arxiv.1708.06833,
title = {On strongly flat and weakly cotorsion modules},
author = {Leonid Positselski and Alexander Slavik},
journal= {arXiv preprint arXiv:1708.06833},
year = {2019}
}
Comments
LaTeX 2e, 51 pages; v.3: section 0.0 inserted in the introduction, some details added in the proofs of theorems 2.6 and 7.7, several references added; v.4: small changes in section 0.1, a reference added at the end of section 0.2; v.5: several misprints corrected, references updated, the numbering of sections shifted to agree with the journal version