ZARISKI TOPOLOGIES ON SKEW BRACES

A. Goswami, T. Dube

Research output: Contribution to journalArticlepeer-review

Abstract

By modifying the usual definition of a prime ideal in a skew brace A somewhat, we define what we call a skew-prime ideal of A, and denote by SpecsA the set of these ideals. We then endow this set with a Zariski topology in a manner akin to how the set of prime ideals of a commutative ring is endowed with the Zariski topology. We characterize the irreducible closed subsets of the resulting topological space, and prove that 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. Denoting the set of all ideals of A by Idl A, it turns out that Idl A, partially ordered by inclusion, is a multiplicative lattice with a certain multiplication introduced here for the first time. We end the paper by observing that Spec(Idl A) is a spectral space.

Original languageEnglish
Pages (from-to)474-482
Number of pages9
JournalPalestine Journal of Mathematics
Volume13
Issue number4
Publication statusPublished - 2024

Keywords

  • Irreducibility
  • Skew brace
  • Skew-prime ideal
  • Spectral space

ASJC Scopus subject areas

  • General Mathematics

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