Abstrakt
Baer's Criterion for Injectivity is a useful tool of the theory of modules. Its dual version (DBC) is known to hold for all right perfect rings, but its validity for the non-right perfect ones is a complex problem (first formulated by C.
Faith [Algebra. II.
Ring Theory, Springer, Berlin, 1976]). Recently, it has turned out that there are two classes of non-right perfect rings: (1) those for which DBC fails in ZFC, and (2) those for which DBC is independent of ZFC.
First examples of rings in the latter class were constructed in [J. Trlifaj, Faith's problem on R-projectivity is undecidable, Proc.
Amer. Math.
Soc.147 (2019), no. 2, 497-504]; here, we show that this class contains all small semiartinian von Neumann regular rings with primitive factors artinian.