$F$-nilpotent rings and permanence properties
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| Soggetti: | |
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| _version_ | 1866914831342239744 |
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| author | Kenkel, Jennifer Maddox, Kyle Polstra, Thomas Simpson, Austyn |
| author_facet | Kenkel, Jennifer Maddox, Kyle Polstra, Thomas Simpson, Austyn |
| contents | We explore the singularity classes $F$-nilpotent, weakly $F$-nilpotent, and generalized weakly $F$-nilpotent under faithfully flat local ring maps. As an application, we show that the loci of primes in a Noetherian ring of prime characteristic which define either weakly $F$-nilpotent or $F$-nilpotent local rings are open with respect to the Zariski topology whenever $R$ is $F$-finite or essentially of finite type over an excellent local ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_01150 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $F$-nilpotent rings and permanence properties Kenkel, Jennifer Maddox, Kyle Polstra, Thomas Simpson, Austyn Commutative Algebra We explore the singularity classes $F$-nilpotent, weakly $F$-nilpotent, and generalized weakly $F$-nilpotent under faithfully flat local ring maps. As an application, we show that the loci of primes in a Noetherian ring of prime characteristic which define either weakly $F$-nilpotent or $F$-nilpotent local rings are open with respect to the Zariski topology whenever $R$ is $F$-finite or essentially of finite type over an excellent local ring. |
| title | $F$-nilpotent rings and permanence properties |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/1912.01150 |