Non-perfect rings and a theorem of Eklof and Shelah

summary:We prove a stronger form, $A^+$, of a consistency result, $A$, due to Eklof and Shelah. $A^+$ concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that $A$ does not hold for left perfect rings

The Dual Baer Criterion for non-perfect rings

Baer's Criterion for Injectivity is a basic tool of the theory of modules and complexes of modules. Its dual version (DBC) is known to hold for all right perfect rings, but its validity for non-right perfect rings is a complex problem (first formulated by Faith in 1976 \cite{F}). 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 \cite{T4}; here, we show that this class contains all small semiartinian von Neumann regular rings with primitive factors artinian.Comment: Revised version for Forum Math., 12 page