대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권1호
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  • Pages.259-266
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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TERMINAL SPACES OF MONOIDS

  • Amartya Goswami (Department of Mathematics and Applied Mathematics University of Johannesburg, National Institute for Theoretical and Computational Sciences (NITheCS))
  • 투고 : 2023.04.26
  • 심사 : 2023.08.02
  • 발행 : 2024.01.31
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초록

The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to r-strongly irreducible r-ideals (endowed with Zariski topologies) of monoids, called terminal spaces. We show that terminal spaces are T0, quasi-compact, and every nonempty irreducible closed subset has a unique generic point. We characterize rarithmetic monoids in terms of terminal spaces. Finally, we provide necessary and sufficient conditions for the subspaces of r-maximal r-ideals and r-prime r-ideals to be dense in the corresponding terminal spaces.

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과제정보

The author would like to express sincere gratitude to the anonymous referee for their meticulous review and invaluable feedback, which made a significant contribution to improving the presentation of the paper.

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