Advanced search
Publication Cover
Communications in Algebra Volume 50, 2022 - Issue 11
Submit an article Journal homepage
101
Views
0
CrossRef citations to date
0
Altmetric
Articles

A Cohen-type theorem for w-Noetherian modules

Ke HuangSchool of Mathematics and Science, Sichuan Normal University, Chengdu, ChinaCorrespondence[email protected]
View further author information
&
Fanggui WangSchool of Mathematics and Science, Sichuan Normal University, Chengdu, ChinaView further author information
Pages 4882-4890 | Received 24 Oct 2021, Accepted 04 May 2022, Published online: 30 May 2022

References

  • Abu-Saymeh, S. (1995). On dimensions of finitely generated modules. Commun. Algebra 23(3):1131–1144. DOI: 10.1080/00927879508825270.
  • Atani, S. E., Saraei, F. E. K. (2008). On generalized distinguished prime submodules. Thai J. Math. 6(2):369–376.
  • Chung, W., Ha, J., Kim, H. (2010). Some remarks on strong Mori domains. Houston J. Math. 38(4):1051–1059.
  • Cho, Y. H. (2000). On distinguished prime submodules. Comm. Korean Math. Soc. 15(3):493–498.
  • Cohen, I. S. (1950). Commutative Rings with restricted minimum conditions. Duke Math. J. 17(1):27–42. DOI: 10.1215/S0012-7094-50-01704-2.
  • Jothilingam, P. (2000). Cohen’s theorem and Eakin-Nagata theorem, revisited. Commun. Algebra 28(10):4861–4866. DOI: 10.1080/00927870008827126.
  • Kaplansky, I. (1974). Commutative Rings (Revised Edition). Chicago and London: University of Chicago Press.
  • Kim, D. K., Lim, J. W. (2020). The Cohen type theorem and the Eakin-Nagata type theorem for S-Noetherian rings, revisited. Rocky Mountain J. Math. 50(2):619–630. DOI: 10.1216/rmj.2020.50.619.
  • Man, S. H., Smith, P. F. (2002). On chains of prime submodules. Isr. J. Math. 127(1):131–155. DOI: 10.1007/BF02784529.
  • McCasland, R. L., Smith, P. F. (1993). Prime submodules of Noetherian modules. Rocky Mountain J. Math. 23(3):1041–1062. DOI: 10.1216/rmjm/1181072540.
  • Naghipour, A. R. (2005). A simple proof of Cohen’s theorem. Amer. Math. Monthly 112(9):825–826. DOI: 10.1080/00029890.2005.11920257.
  • Nishitani, I. (2006). A Cohen-type theorem for Artinian modules. Arch. Math. 87(3):206–210. DOI: 10.1007/s00013-006-1617-x.
  • Parkash, A., Kour, S. (2021). On Cohen’s theorem for modules. Indian J Pure Appl Math. 52(3):869–871. DOI: 10.1007/s13226-021-00101-z.
  • Smith, P. F. (1994). Concerning a theorem of I. S. Cohen. XIth National Conference of Algebra (Constanta, 1994), An. Stiint. Univ. Ovidius Constanta Ser. Mat. 2:160–167.
  • Wang, F. G. (2010). Finitely presented type modules and w-coherent rings. J. Sichuan Normal Univ. 33(1):1–9. DOI: 10.3969/j.issn.1001-8395.2010.01.001.
  • Wang, F. G., Kim, H. (2016). Foundations of Commutative Rings and Their Modules. Singapore: Springer Nature Singapore Pvt. Ltd.
  • Wang, F. G., McCasland, R. L. (1997). On w-modules over strong Mori domains. Commun. Algebra 25(4):1285–1306. DOI: 10.1080/00927879708825920.
  • Yin, H. Y. (2007). Prime Submodules over Commutative Rings (in Chinese). Thesis. Sichuan Normal University.
  • Yin, H. Y., Wang, F. G., Chen, Y. H. (2007). GV-ideals and prime submodules (in Chinese). J. Sichuan Normal Univ. 30(2):160–163. DOI: 10.3969/j.issn.1001-8395.2007.02.010.
  • Yin, H. Y., Wang, F. G., Zhu, X. S., Chen, Y. H. (2011). w-modules over commutative rings. J. Korean Math. Soc. 48(1):207–222. DOI: 10.4134/JKMS.2011.48.1.207.
  • Zhou, D. C., Kim, H., Hu, K. (2021). A Cohen-type theorem for w-Artinian modules. J. Algebra Appl. 20(06):2150106. DOI: 10.1142/S0219498821501061.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.