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Spectral topologies on skew braces

Themba DubeAmartya Goswami
Dec 2022
摘要
Using a new definition of a prime ideal of a skew brace A, on set Spec A ofprime ideals of A we endow a spectral topology (in the sense of Grothendieck).We characterize irreducible closed subsets of Spec A and prove everyirreducible closed subset of the space has a unique generic point. We give asufficient condition for the space to be Noetherian. We study continuous mapsbetween such spaces, and finally, we prove that Spec(Idl A) is a spectralspace, where Idl A is the set of all ideals of A.
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