##
**Von Neumann regular rings and the Whitehead property of modules.**
*(English)*
Zbl 0728.16005

The author continues the study of Ext-rings (rings such that each (left) module has the Whitehead property) initiated in his monograph [Associative Rings and the Whitehead Property of Modules (1990; Zbl 0692.16017)] in which it was proved that these rings fall into two classes: the artinian and the (Von Neumann) regular ones. However, no examples of non-completely reducible regular Ext-rings are known. In the paper under review, the author proves that a class of promising candidates fails to provide such examples and then goes on to show that, in fact, the assertion “Every regular left or right Ext-ring is completely reducible” is consistent with ZFC.

Reviewer: J.L.Gómez Pardo (Murcia)

### MSC:

16E50 | von Neumann regular rings and generalizations (associative algebraic aspects) |

16S70 | Extensions of associative rings by ideals |

03E35 | Consistency and independence results |

16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |