Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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TRIVIAL RING EXTENSION WITH EPI-DCC/DCCd ON IDEALS

  • Mohamed Khalifa (Department of Technology University of Sousse Higher Institute of Transport and Logistics)
  • Received : 2025.07.08
  • Accepted : 2026.01.13
  • Published : 2026.07.31
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Abstract

Let A be an integral domain, E a torsion-free and divisible A-module. We prove that the trivial ring extension A ∝ E satisfies epi-DCC on ideals (respectively DCCd on ideals / is an isoartinian ring) if and only if E satisfies epi-DCC on submodules (respectively strongly DCCd on submodules / is an isoartinian module). Let D be an integral domain with quotient field K. We deduce that the ring D ∝ K satisfies epi-DCC on ideals (respectively DCCd on ideals / is an isoartinian ring) if and only if D is a semi-local principal ideal domain.

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