Skip to main content Accessibility help
×
Home

A Note on Division Algebras

  • I. N. Herstein (a1) and A. Ramer (a2)

Extract

In this note we prove some results on the intersection properties of maximal subfields of division algebras which are finite dimensional over their centers. These results indicate that we can get very small intersections with any subalgebra if we use the appropriate maximal subfields. As a consequence of our first theorem, we obtain some theorems which are known and some which can be obtained from these known theorems (see, for instance, Theorem 3, Chapter VII in [3]). The proofs of these known results given here are very elementary and are quite different from the ones in the literature.

    • 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 Note on Division Algebras
      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 Note on Division Algebras
      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 Note on Division Algebras
      Available formats
      ×

Copyright

References

Hide All
1. Artin, E., Galois theory (Notre Dame Mathematical Lectures No. 2, 1946).
2. Herstein, I. N., Non-commutative rings (Carus Monograph No. 15, 1968).
3. Nathan, Jacobson, Structure of rings (A.M.S. Colloquium Series, No. XXXVII, 1956, 1964).
4. Irving, Kaplansky, Fields and rings (Chicago Lectures in Mathematics, 1969).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

A Note on Division Algebras

  • I. N. Herstein (a1) and A. Ramer (a2)

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