On J-Noetherian modules and J-coherent modules
Younes El Haddaoui\,^1 and Hwankoo Kim\,^2
\,^{1} Department of Mathematics, Faculty of Science and Technology, Fez, Morocco.
\,^{2} Division of Computer Engineering, Hoseo University, Asan, 31499, Republic of Korea.
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Pages 1-14 | Received 10 February 2025, Accepted 01 June 2025, Published 19 July 2026
Abstract
This paper continues the study of the recently introduced notion of J-ideals by Khashan and Bani-Ata, extending it to a module-theoretic and homological framework. First, we introduce and investigate J-injective modules, providing a Baer-type characterization and studying their relation to J-torsion-free and J-divisible modules. We then define and examine J-Noetherian modules and rings, showing that many classical properties such as the ascending chain condition and the Cartan–Eilenberg–Bass Theorem admit J-analogues. Finally, we develop the theory of J-flat and J-coherent modules, characterizing J-coherent rings through homological conditions and examples. Our results reveal that many homological behaviors persist in this broader setting, shedding light on the structural richness of the J-ideal framework.
Keywords: J-submodule, J-injective module, J-Noetherian module, J-Noetherian ring, J-flat module, J-coherent module, J-coherent ring.
MSC numbers: 13A15, 13A18, 13F05, 13G05, 13C20.
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