Jan Trlifaj, Charles
University Prague
Faith's
problem on R-projectivity is undecidable
Abstract: In
1976, Faith asked for a characterization of the rings R
such that each R-projective module is projective, that is,
the Dual Baer Criterion holds in Mod-R. Such rings were
called right testing. Sandomierski proved that each right
perfect ring is right testing. Puninski et al. have
recently shown for a number of non-right perfect rings
that they are not right testing (in ZFC), and noticed the
consistency with ZFC of the statement `each right testing
ring is right perfect.'