Ir al contenido

Documat


Zariski topology on the spectrum of fuzzy classical primary submodules

  • Panpho, Phakakorn [1] ; Yiarayong, Pairote [1]
    1. [1] Pibulsongkram Rajabhat University

      Pibulsongkram Rajabhat University

      Tailandia

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 333-343
  • Idioma: inglés
  • DOI: 10.4995/agt.2022.17427
  • Enlaces
  • Resumen
    • Let R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.

  • Referencias bibliográficas
    • J. Abuhlail, A Zariski topology for modules, Communications in Algebra 39 (2011), 4163-4182. https://doi.org/10.1080/00927872.2010.519748
    • M. Alkan and Y. Tiras, Projective modules and prime submodules, Czechoslovak Math. J. 56 (2006), 601-611. https://doi.org/10.1007/s10587-006-0041-5
    • R. Ameri and R. Mahjoob, Spectrum of prime $L$-submodules, Fuzzy Sets Syst. 159 (2008), 1107-1115. https://doi.org/10.1016/j.fss.2007.08.011
    • R. Ameri and R. Mahjoob, Spectrum of prime fuzzy hyperideals, Iranian Journal of Fuzzy Systems 6, no. 4 (2009), 61-72.
    • R. Ameri and R. Mahjoob, Some topological properties of spectrum of fuzzy submodules, Iranian Journal of Fuzzy Systems 14, no. 1 (2017), 77-87.
    • R. Ameri, R. Mahjoob and M. Mootamani, The Zariski topology on the spectrum of prime L-submodules, Soft Comput. 12 (2008), 901-908. https://doi.org/10.1007/s00500-007-0259-7
    • A. Azizi, Prime submodules and flat modules, Acta Math. Sin. (Eng. Ser.) 23 (2007), 47-152. https://doi.org/10.1007/s10114-005-0813-0
    • J. Castro, J. Rios and G. Tapia, Some aspects of Zariski topology for multiplication modules and their attached frames and quantales, J. Korean...
    • J. Dauns, Prime modules, J. Reine Angew Math. 298 (1978), 156-181. https://doi.org/10.1515/crll.1978.298.156
    • A. Y. Darani and S. Motmaen, Zariski topology on the spectrum of graded classical prime submodules, Appl. Gen. Topol. 14, no. 2 (2013), 159-169....
    • J. Goswami and H. K. Saikia, On the spectrum of weakly prime submodule, Thai Journal of Mathematics 19, no. 1 (2021), 51-58.
    • W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst. 8 (1982), 133-139. https://doi.org/10.1016/0165-0114(82)90003-3
    • C. P. Lu, The Zariski topology on the prime spectrum of a module, Houston J. Math. 25 (1999), 417-432.
    • C. V. Negoita and D. A. Ralescu, Application of fuzzy systems analysis, Birkhauser, Basel, 1975. https://doi.org/10.1007/978-3-0348-5921-9
    • H. A. Toroghy and S. S. Pourmortazavi, On the prime spectrum of modules, Miskolc Mathematical Notes 16, no. 2 (2015), 1233-1242. https://doi.org/10.18514/MMN.2015.1102
    • H. A. Toroghy and R. O. Sarmazdeh, On the prime spectrum of a module and Zariski topologies, Communications in Algebra 38 (2010), 4461-4475....
    • L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
    • K. A. Zoubi and M. Jaradat, The Zariski topology on the graded classical prime spectrum of a graded module over a graded commutative ring,...

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno