The strongly flat dimension of modules and rings
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916403225821184 |
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| author | Bouziri, Ayoub |
| author_facet | Bouziri, Ayoub |
| contents | Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Positselski and Slávik 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The strongly flat dimension of modules and rings Bouziri, Ayoub Commutative Algebra Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Positselski and Slávik 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. |
| title | The strongly flat dimension of modules and rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2409.13487 |