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 language | English |
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Pages (from-to) | 474-482 |
Number of pages | 9 |
Journal | Palestine Journal of Mathematics |
Volume | 13 |
Issue number | 4 |
Publication status | Published - 2024 |
Keywords
- Irreducibility
- Skew brace
- Skew-prime ideal
- Spectral space
ASJC Scopus subject areas
- General Mathematics