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arXiv · 1708.06833

On strongly flat and weakly cotorsion modules

Leonid Positselski·Alexander Slavik
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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.

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Leonid Positselski, Alexander Slavik. 2018-08-08. On strongly flat and weakly cotorsion modules. https://doi.org/10.1007/s00209-018-2116-z

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