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Seminario MALGA Padova Verona - Moduli Algebre Anelli: “Faith's problem on R-projectivity is undecidable”

Giovedì 24 Maggio 2018, ore 11:30 - Aula 1BC50 - Jan Trlifaj

ARGOMENTI: Seminars

Giovedì 24 Maggio 2018 alle ore 11:30 in Aula 1BC50, Jan Trlifaj (Charles University Praha, Czech Republic) terrà un seminario dal titolo “Faith's problem on R-projectivity is undecidable“, nell'ambito del Seminario Padova-Verona MALGA - Moduli Algebre Anelli.

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”. We prove the complementing consistency result: the existence of a right testing, but non-right perfect ring is also consistent with ZFC. Thus the answer to the Faith's question above is independent of ZFC. Moreover, for each cardinal c, we provide examples of non-right perfect rings R such that the Dual Baer Criterion holds (in ZFC) for all at most c-generated R-modules.