The strongly flat dimension of modules and rings
Commutative Algebra
2024-09-23 v1
Abstract
Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Positselski and Sl\'avik introduced the concepts of S-strongly flat modules and S-weakly cotorsion R-modules, and they showed that these concepts are useful in describing flat modules and Enochs cotorsion modules over commutative rings (see the discussion in [13, Section 1.1]). In this paper, we introduce a homological dimension, called the S-strongly flat dimension, for modules and rings. These dimensions measure how far away a module M is from being S-strongly flat and how far a ring R is from being S-almost semisimple. The relations between the S-strongly flat dimension and other dimensions are discussed.
Cite
@article{arxiv.2409.13487,
title = {The strongly flat dimension of modules and rings},
author = {Ayoub Bouziri},
journal= {arXiv preprint arXiv:2409.13487},
year = {2024}
}