k-spaces of non-domain-valued geometric points

Amartya Goswami

Ayuda

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
DOI: 10.4995/agt.2024.19887
Enlaces
- Texto completo
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.
Referencias bibliográficas
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