Skip to main content
×
×
Home

A Foundation of Torsion Theory for Modules Over General Rings

  • Akira Hattori (a1)
Extract

When we consider modules A over a ring R which is not a commutative integral domain, the usual torsion theory becomes somewhat inadequate, since zero-divisors of R are disregarded and since the torsion elements of A do not in general form a submodule. In this paper we shall try to remedy such defects by modifying the fundamental notions such as torsion modules, divisible modules, etc.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A Foundation of Torsion Theory for Modules Over General Rings
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A Foundation of Torsion Theory for Modules Over General Rings
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A Foundation of Torsion Theory for Modules Over General Rings
      Available formats
      ×
Copyright
References
Hide All
[1] Asano, K., Theory of Rings and Ideals, Kyoritu Shuppan, 1949.
[2] Auslander, M. and Buchsbaum, D. A., Homological dimension in local rings, Trans. Amer. Math. Soc., 85 (1957), 390405.
[3] Cartan, H. and Eilenberg, S., Homological Algebra, Princeton Univ. Press, 1956.
[4] Harada, M., Note on the dimension of modules and algebras, Journ. Inst. of Polyt., Osaka City Univ., 7 (1956), 1727.
[5] Ikeda, M. and Nakayama, T., On some characteristic properties of quasi-Frobenius and regular rings, Proc. Amer. Math. Soc., 5 (1954), 1519.
[6] Jacobson, N., The Theory of Rings, Amer. Math. Soc. Math. Surveys, v. 1, 1943.
[7] Kaplansky, J., Infinite Abelian Groups, Univ. of Michigan Publ. in Mathematics, No. 2, 1954.
[8] Nakano, T., A nearly semisimple ring, Comment. Math. Univ. St. Pauli, 7 (1959), 2733.
[9] Nakayama, T. and Azumaya, G., Algebra II, Iwanami, 1954.
[10] von Neumann, J., On negular rings, Proc. Nat. Acad. Sci., 22 (1936), 707713,
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed