Startseite The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring
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The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring

  • Malik Jaradat und Khaldoun Al-Zoubi ORCID logo EMAIL logo
Veröffentlicht/Copyright: 4. Oktober 2023
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Georgian Mathematical Journal
Aus der Zeitschrift Georgian Mathematical Journal Band 31 Heft 2

Abstract

Let G be a group. Let R be a G-graded commutative ring and let M be a graded R-module. A proper graded submodule Q of M is called a graded quasi-primary submodule if whenever r ∈ h ⁢ ( R ) and m ∈ h ⁢ ( M ) with r ⁢ m ∈ Q , then either r ∈ Gr ( ( Q : R M ) ) or m ∈ Gr M ⁡ ( Q ) . The graded quasi-primary spectrum qp . Spec g ( M ) is defined to be the set of all graded quasi-primary submodules of M. In this paper, we introduce and study a topology on qp . Spec g ( M ) , called the quasi-Zariski topology, and investigate the properties of this topology and some conditions under which ( qp . Spec g ( M ) , q . τ g ) is a Noetherian, spectral space.

Keywords: Graded quasi-Zariski topology; graded quasi-primary spectrum; graded quasi-primary submodule
MSC 2020: 13A02; 16W50

References

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Received: 2023-02-15
Revised: 2023-05-17
Accepted: 2023-05-22
Published Online: 2023-10-04
Published in Print: 2024-04-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On skew derivations and antiautomorphisms in prime rings
  3. On the non-triviality of anisotropic Roumieu Gelfand–Shilov spaces and inclusion between them
  4. Solution of generalized fractional kinetic equations with generalized Mathieu series
  5. The generalized Drazin inverse of an operator matrix with commuting entries
  6. Asymptotic analysis of fundamental solutions of hypoelliptic operators
  7. Calculation of Reynolds equation for the generalized non-Newtonian fluids and its asymptotic behavior in a thin domain
  8. Double lacunary statistical convergence of Δ-measurable functions on product time scales
  9. On ρ-statistical convergence in neutrosophic normed spaces
  10. On the comparison of translation invariant convex differentiation bases
  11. The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring
  12. Some classes of topological spaces and the space of G-permutation degree
  13. BV capacity and perimeter in abstract Wiener spaces and applications
  14. New approach on the study of operator matrix
  15. Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms
  16. Localization operators and inversion formulas for the Dunkl–Weinstein–Stockwell transform
https://doi.org/10.1515/gmj-2023-2075
Schlagwörter für diesen Artikel
Graded quasi-Zariski topology; graded quasi-primary spectrum; graded quasi-primary submodule

Artikel in diesem Heft

  1. Frontmatter
  2. On skew derivations and antiautomorphisms in prime rings
  3. On the non-triviality of anisotropic Roumieu Gelfand–Shilov spaces and inclusion between them
  4. Solution of generalized fractional kinetic equations with generalized Mathieu series
  5. The generalized Drazin inverse of an operator matrix with commuting entries
  6. Asymptotic analysis of fundamental solutions of hypoelliptic operators
  7. Calculation of Reynolds equation for the generalized non-Newtonian fluids and its asymptotic behavior in a thin domain
  8. Double lacunary statistical convergence of Δ-measurable functions on product time scales
  9. On ρ-statistical convergence in neutrosophic normed spaces
  10. On the comparison of translation invariant convex differentiation bases
  11. The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring
  12. Some classes of topological spaces and the space of G-permutation degree
  13. BV capacity and perimeter in abstract Wiener spaces and applications
  14. New approach on the study of operator matrix
  15. Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms
  16. Localization operators and inversion formulas for the Dunkl–Weinstein–Stockwell transform
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