k-spaces of non-domain-valued geometric points

• Goswami, Amartya ^[1]
  1. [1] University of Johannesburg

     University of Johannesburg

     City of Johannesburg, Sudáfrica

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 2, 2024, págs. 375-383
• Idioma: inglés
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• Resumen

  • The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a k-algebra and this new “k-space” becomes a generalization of the corresponding Zariski space. We prove that a k-space is T0, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such k-spaces. We conclude with a question about the construction of a sheaf of k-spaces similar to affine schemes.