On von Neumann regular rings. XV. (English) Zbl 0685.16009

[Part XIV cf. An. Univ. Timişoara, Ştiinţe Mat. 25, 75-88 (1987; Zbl 0641.16008).]
In the first part of this paper, certain subclasses of regular rings are characterized. Two typical results are: (1) If A is a ring whose essential ideals are two-sided, then A is regular iff A is semi-prime and every simple left module is flat. (2) A is strongly regular iff every simple right module is flat and every complement left ideal is two-sided. The second part is concerned with rings having a classical quotient ring and with divisible modules. Semi-simple Artinian rings, Goldie rings and duo ring also make their appearance.
Reviewer: H.H.Storrer


16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16D50 Injective modules, self-injective associative rings
16L60 Quasi-Frobenius rings
16D40 Free, projective, and flat modules and ideals in associative algebras


Zbl 0641.16008