Abstract
Regular, right self-injective rings are considered. We settle the question of when such a ring is a right V-ring, i.e., when each simple right module over the ring is injective. It is proved that a regular, right self-injective V-ring of the power of the continuum has a bounded nilpotency index.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. R. Goodearl,Von Neumann Regular Rings, Pitman, London (1979).
J. M. Goursaud and J. Valette, “Sur l'enveloppe injective des anneaux de groupes reguliers,”Bull. Soc. Math. France,103, 91–102 (1975).
G. Baccella, “Von Neumann regularity ofV-rings with artinian primitive factor rings,”Proc. Am. Math. Soc.,103, No. 3, 747–749 (1988).
K. I. Beidar and A. V. Mikhalev, “Semiprime rings with bounded nilpotency indices,”Trudy Sem. Petrovski,13, 247–249 (1988).
B. L. Osofsky, “Cyclic injective modules of full linear ring,”Proc. Am. Math. Soc.,17, No. 1, 247–253 (1966).
J. M. Goursaud and L. Jeremy, “Une notion de rang les facteurs reguliers auto-injectifs a droite,”Commun. Algebra,5, No. 8, 829–839 (1977).
K. R. Goodearl and J. Moncasi, “Cancellation of finitely generated modules over regular rings,”Osaka J. Math.,26, No. 3, 679–685 (1989).
A. Tarski “Sur la decomposition des ensembles en sousensembles presque disjoints,”Fund. Math.,12, 188–205 (1928).
Bourbaki,Algèbre, Hermann, Paris (1960).
Additional information
Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 564–575, September–October, 1994.
Rights and permissions
About this article
Cite this article
Tyukavkin, D.V. Regular self-injective rings andV-rings. Algebr Logic 33, 315–321 (1994). https://doi.org/10.1007/BF00739572
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00739572