# zbMATH — the first resource for mathematics

Regular self-injective rings and $$V$$-rings. (English. Russian original) Zbl 0841.16009
Algebra Logic 33, No. 5, 315-321 (1994); translation from Algebra Logika 33, No. 5, 564-575 (1994).
Summary: 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 bounded nilpotency index.

##### MSC:
 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16D50 Injective modules, self-injective associative rings
Full Text:
##### References:
 [1] K. R. Goodearl,Von Neumann Regular Rings, Pitman, London (1979). [2] J. M. Goursaud and J. Valette, ?Sur l’enveloppe injective des anneaux de groupes reguliers,?Bull. Soc. Math. France,103, 91-102 (1975). · Zbl 0309.16011 [3] G. Baccella, ?Von Neumann regularity ofV-rings with artinian primitive factor rings,?Proc. Am. Math. Soc.,103, No. 3, 747-749 (1988). · Zbl 0659.16008 [4] K. I. Beidar and A. V. Mikhalev, ?Semiprime rings with bounded nilpotency indices,?Trudy Sem. Petrovski,13, 247-249 (1988). · Zbl 0682.16004 [5] B. L. Osofsky, ?Cyclic injective modules of full linear ring,?Proc. Am. Math. Soc.,17, No. 1, 247-253 (1966). · Zbl 0144.02402 [6] 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). · Zbl 0357.16008 [7] K. R. Goodearl and J. Moncasi, ?Cancellation of finitely generated modules over regular rings,?Osaka J. Math.,26, No. 3, 679-685 (1989). · Zbl 0716.16007 [8] A. Tarski ?Sur la decomposition des ensembles en sousensembles presque disjoints,?Fund. Math.,12, 188-205 (1928). · JFM 54.0092.02 [9] Bourbaki,Algèbre, Hermann, Paris (1960).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.