Cleft extensions of rings and singularity categories
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915445176532992 |
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| author | Kostas, Panagiotis |
| author_facet | Kostas, Panagiotis |
| contents | This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft extensions of rings. This setting includes triangular matrix rings, trivial extension rings and tensor rings, among others. Under certain conditions, we prove singular equivalences between the algebras in a cleft extension, unifying an abundance of known results. Moreover, we compare the big singularity categories of cleft extensions of rings in the sense of Krause. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cleft extensions of rings and singularity categories Kostas, Panagiotis Representation Theory Category Theory Rings and Algebras 16E, 16E30, 16E65, 16E10, 16G50, 18E, 18G80 This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft extensions of rings. This setting includes triangular matrix rings, trivial extension rings and tensor rings, among others. Under certain conditions, we prove singular equivalences between the algebras in a cleft extension, unifying an abundance of known results. Moreover, we compare the big singularity categories of cleft extensions of rings in the sense of Krause. |
| title | Cleft extensions of rings and singularity categories |
| topic | Representation Theory Category Theory Rings and Algebras 16E, 16E30, 16E65, 16E10, 16G50, 18E, 18G80 |
| url | https://arxiv.org/abs/2409.07919 |