Spectral topologies on skew braces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908338358321152 |
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| author | Dube, Themba Goswami, Amartya |
| author_facet | Dube, Themba Goswami, Amartya |
| contents | Using a new definition of a prime ideal of a skew brace A, on set Spec A of prime ideals of A we endow a spectral topology (in the sense of Grothendieck). We characterize irreducible closed subsets of Spec A and prove every irreducible closed subset of the space has a unique generic point. We give a sufficient condition for the space to be Noetherian. We study continuous maps between such spaces, and finally, we prove that Spec(Idl A) is a spectral space, where Idl A is the set of all ideals of A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12928 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectral topologies on skew braces Dube, Themba Goswami, Amartya Rings and Algebras 16T25, 08A99 Using a new definition of a prime ideal of a skew brace A, on set Spec A of prime ideals of A we endow a spectral topology (in the sense of Grothendieck). We characterize irreducible closed subsets of Spec A and prove every irreducible closed subset of the space has a unique generic point. We give a sufficient condition for the space to be Noetherian. We study continuous maps between such spaces, and finally, we prove that Spec(Idl A) is a spectral space, where Idl A is the set of all ideals of A. |
| title | Spectral topologies on skew braces |
| topic | Rings and Algebras 16T25, 08A99 |
| url | https://arxiv.org/abs/2212.12928 |