Ir al contenido

Documat


Proper spaces are spectral

  • 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. 24, Nº. 1, 2023, págs. 95-99
  • Idioma: inglés
  • DOI: 10.4995/agt.2023.17800
  • Enlaces
  • Resumen
    • Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we give a new self-contained and constructible topology-independent proof of the fact that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.

  • Referencias bibliográficas
    • A. Abbasi and D. Hassanzadeh-Lelekaami, Modules and spectral spaces, Comm. Algebra 40, no. 11 (2012), 4111-4129. https://doi.org/10.1080/00927872.2011.602273
    • N. Bezhanishvili and W. H. Holliday, Choice-free Stone duality, J. Symb. Log. 85 (2020), 109-148. https://doi.org/10.1017/jsl.2019.11
    • M. Dickmann, N. Schwartz, and M. Tressel, Spectral spaces, Cambridge Univ. Press, 2019. https://doi.org/10.1017/9781316543870
    • D. E. Dobbs, R. Fedder, and M. Fontana, Abstract Riemann surfaces of integral domains and spectral spaces, Annali Mat. Pura Appl. 148 (1987),...
    • D. E. Dobbs and M. Fontana, Kronecker function rings and abstract Riemann surfaces, J. Algebra 99 (1986), 263-274. https://doi.org/10.1016/0021-8693(86)90067-0
    • T. Dube and A. Goswami, Ideal spaces: an extension of structure spaces of a ring, J. Algebra Appl., to appear.
    • C. A. Finocchiaro, M. Fontana, and D. Spirito, A topological version of Hilbert's Nullstellensatz, J. Algebra 461 (2016), 25-41. https://doi.org/10.1016/j.jalgebra.2016.04.020
    • C. A. Finocchiaro, M. Fontana, and D. Spirito, New distinguished classes of spectral spaces: a survey, in: Multiplicative ideal theory and...
    • C. Finocchiaro and D. Spirito, Suprema in spectral spaces and the constructible closure, New York J. Math. 26 (2020), 1064-1092.
    • D. Harris, Universal quasi-compact T_1 spaces, General Topology and Appl. 3 (1973), 291-318. https://doi.org/10.1016/0016-660X(73)90018-4
    • M. Hochster, Prime ideal structure in commutative rings, Trans. Am. Math. Soc. 142 (1969), 43-60. https://doi.org/10.1090/S0002-9947-1969-0251026-X
    • J. McDonald and K. Yamamoto, Choice-free duality for orthocomplemented lattices by means of spectral spaces, Algebra Universalis 83 (2022),...
    • H. A. Priestley, Intrinsic spectral topologies, in: Papers on general topology and applications (Flushing, NY, 1992), 728, 78-95, New York...
    • S. Ray, Closure operations, continuous valuations on monoids and spectral spaces, J. Algebra Appl. 19, no. 1 (2020), 2050006. https://doi.org/10.1142/S0219498820500061

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno