Acknowledgement
The authors would like thank referees for useful comments.
References
- D. D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra, 30(2002), 4407-4416. https://doi.org/10.1081/AGB-120013328
- M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley(1969).
- W. Chung, J. Ha and H. Kim, Some remarks on strong Mori domains, Houston J. Math., 38(4)(2012), 1051-1059.
- I. S. Cohen, Commutative rings with restricted minimum condition, Duke Math. J., 17(1950), 27-42. https://doi.org/10.1215/S0012-7094-50-01704-2
- P. Jothilingam, Cohen's theorem and Eakin-Nagata theorem revisited, Comm. Algebra, 28(10)(2000), 4861-4866. https://doi.org/10.1080/00927870008827126
- H. Kim, M. O. Kim and J. W. Lim, On S-strong Mori domains, J. Algebra, 416(2014), 314-332. https://doi.org/10.1016/j.jalgebra.2014.06.015
- H. Kim, N. Mahdou and Y. Zahir, S-Noetherian in bi-amalgamations, Bull. Korean Math. Soc., 58(4)(2021), 1021-1029.
- J. W. Lim, A note on S-Noetherian domains, Kyungpook Math. J., 55(2015), 507-514. https://doi.org/10.5666/KMJ.2015.55.3.507
- Z. Liu, On S-Noetherian rings, Arch. Math. (Brno), 43(2007), 55-60.
- R. L. McCasland and P. F. Smith, Prime submodules of Noetherian modules, Rocky Mountain J. Math., 23(3)(1993), 1041-1062. https://doi.org/10.1216/rmjm/1181072540
- A. Parkash and S. Kour, On Cohen's theorem for modules, Indian J. Pure Appl. Math., 52(4) (2021), 869-871. https://doi.org/10.1007/s13226-021-00101-z
- P. F. Smith, Concerning a theorem of I. S. Cohen. XIth National Conference of Algebra (Constanta, 1994), An. Stiint. Univ. Ovidius Constanta Ser. Mat., 2(1994), 160-167.
- F. G. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Singapore, Springer(2016).
- F. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra, 25(1997), 1285-1306. https://doi.org/10.1080/00927879708825920
- H. Yin, F. G. Wang, X. Zhu and Y. Chen, w-modules over commutative rings, J. Korean Math. Soc., 48(1)(2011), 207-222. https://doi.org/10.4134/JKMS.2011.48.1.207
- J. Zhang, F. G. Wang and H. Kim, Injective modules over w-Noetherian rings, II, J. Korean Math. Soc., 50(6)(2013), 1051-1066. https://doi.org/10.4134/JKMS.2013.50.5.1051