The Dual Baer Criterion for non-perfect rings

  • 1 Department of Algebra, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
Jan TrlifajORCID iD: https://orcid.org/0000-0001-5773-8661

Abstract

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, 2, 497–504]; here, we show that this class contains all small semiartinian von Neumann regular rings with primitive factors artinian.

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