대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
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  • Pages.1-9
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON NOETHERIAN PSEUDO-PRIME SPECTRUM OF A TOPOLOGICAL LE-MODULE

  • Anjan Kumar Bhuniya (Department of Mathematics Visva-Bharati) ;
  • Manas Kumbhakar (Department of Mathematics Nistarini College)
  • 투고 : 2021.02.14
  • 심사 : 2022.06.15
  • 발행 : 2023.01.31
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초록

An le-module M over a commutative ring R is a complete lattice ordered additive monoid (M, ⩽, +) having the greatest element e together with a module like action of R. This article characterizes the le-modules RM such that the pseudo-prime spectrum XM endowed with the Zariski topology is a Noetherian topological space. If the ring R is Noetherian and the pseudo-prime radical of every submodule elements of RM coincides with its Zariski radical, then XM is a Noetherian topological space. Also we prove that if R is Noetherian and for every submodule element n of M there is an ideal I of R such that V (n) = V (Ie), then the topological space XM is spectral.

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