AbstractBaer’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, 2, 497–504];here, we show that this class contains all small semiartinian von Neumann regular rings with primitive factors artinian.
Forum Mathematicum – de Gruyter
Published: May 1, 2020
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