Skip to main content Accessibility help
×
Home

Directed graphs and nilpotent rings

  • A. V. Kelarev (a1)

Abstract

Suppose that a ring is a sum of its nilpotent subrings. We use directed graphs to give new conditions sufficient for the whole ring to be nilpotent.

    • 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.

      Directed graphs and nilpotent 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.

      Directed graphs and nilpotent 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.

      Directed graphs and nilpotent rings
      Available formats
      ×

Copyright

References

Hide All
[1]Bahturin, Yu. A. and Giambruno, A., ‘Identities of sums of commutative subalgebrasRend. Circ. Mat. Palermo (2) 43 (1994)(2), 250258.
[2]Bahturin, Yu. A. and Kegel, O. H., ‘Lie algebras which are universal sums of abelian subalgebras’, Comm. Algebra 23 (1995), 29752990.
[3]Beidar, K. I. and Mikhalev, A. V., ‘Generalized polynomial identities and rings which are sums of two subrings’, Algebra i Logika 34 (1995)(1), 311.
[4]Bokut', L. A., ‘Embeddings in simple associative algebras’, Algebra i Logika 15 (1976) (2), 117142.
[5]Ferrero, M. and Puczyłowski, E. R., ‘On rings which are sums of two subrings’, Arch. Math. (Basel) 53 (1989), 410.
[6]Fukshansky, A., ‘The sum of two locally nilpotent rings may contain a non-commutative free subring’, Proc. Amer. Math. Soc., to appear.
[7]Herstein, I. N. and Small, L. W., ‘Nil rings satisfying certain chain conditions’, Canad. J. Math. 16 (1964), 771776.
[8]Kegel, O. H., ‘Zur Nilpotenz gewisser assoziativer Ringe’, Math. Ann. 149 (1962/1963), 258260.
[9]Kegel, O. H., ‘On rings that are sums of two subrings’, J. Algebra 1 (1964), 103109.
[10]Kelarev, A. V., ‘A sum of two locally nilpotent rings may be not nil’, Arch. Math. (Basel) 60 (1993), 431435.
[11]Kelarev, A. V., ‘A primitive ring which is a sum of two Wedderburn radical subrings’, Proc. Amer. Math. Soc. 125 (1997), 21912193.
[12]Kelarev, A. V., ‘An answer to a question of Kegel on sums of rings’, Canad. Math. Bull. 41 (1998), 7980.
[13]Kelarev, A. V. and McConnell, N. R., ‘Two versions of graded rings’, Publ. Math. (Debrecen) 47 (1995) (3–4), 219227.
[14]Kepczyk, M. and Puczyłowski, E. R., ‘On radicals of rings which are sums of two subrings’. Arch. Math. (Basel) 66 (1996), 812.
[15]Kepczyk, M. and Puczyłowski, E. R., ‘Rings which are sums of two subrings’, J. Pure Appl. Algebra. to appear.
[16]Puczyłowski, E. R., ‘Some questions concerning radicals of associative rings’, Theory of Radicals, Szekszárd, 1991, Coll. Math. Soc. János Bolyai 61 (1993), 209227.
[17]Salwa, A., ‘Rings that are sums of two locally nilpotent subrings’, Comm. Algebra 24 (1996)(12), 39213931.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

Directed graphs and nilpotent rings

  • A. V. Kelarev (a1)

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