대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제62권1호
  • /
  • Pages.15-25
  • /
  • 2025
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE HOMOGENEOUS SPECTRUM OF A GRADED COMMUTATIVE RING BY TORSION GROUP

  • Mohamed Aqalmoun (Department of Mathematics Higher Normal School Sidi Mohamed Ben Abdellah University) ;
  • Yassir Mata (Department of Mathematics Higher Normal School Sidi Mohamed Ben Abdellah University)
  • 투고 : 2023.09.26
  • 심사 : 2024.09.26
  • 발행 : 2025.01.31
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초록

Let G be a torsion abelian group and let R be a G-graded commutative ring. In this paper, we identify the homogeneous prime ideals of R in terms of prime ideals of Re. Precisely, we show that the map P ↦ P ∩ Re is a homeomorphism between the homogeneous prime spectrum of R and the prime spectrum of Re with respect to Zariski topology.

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과제정보

This work was supported by the National Center for Scientific and Technical Research (CNRST) under the "PhD-ASsociate Scholarship - PASS" Program.

참고문헌

  1. M. Aqalmoun, The homogeneous spectrum of a ℤ2-graded commatatioe ring, Beitr. Algebra Geom. 65 (2024), no. 3, 511-523. https://doi.org/10.1007/s13366-023-00703-0
  2. W. Heinzer and M. Roitman, The homogeneous spectrum of a graded commatatioe ring, Proc. Amer. Math. Soc. 130 (2002), no. 6, 1573-1580. https://doi.org/10.1090/S0002-9939-01-06231-1
  3. C. Năstăsescu and F. M. J. Van Oystaeyen, Graded Ring Theory, North-Holland Mathematical Library, 28, North-Holland, Amsterdam, 1982.
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  6. A. Yousefian Darani and S. Motmaen, Zariski topology on the spectrum of graded classical prime submodules, Appl. Gen. Topol. 14 (2013), no. 2, 159-169. https://doi.org/10.4995/agt.2013.1586