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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.

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)
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