报告人：Jan Trlifaj
报告地点：数学与统计学院104室
报告时间：2018年05月07日星期一10:00-11:00
邀请人：
报告摘要：
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.
主讲人简介：
Professor Dr. Jan Trlifaj is working at Faculty of Mathematics and Physics, Charles University, Prague, Czech. His research interests include Algebra (module and representation theory, commutative and homological algebra), logic (model- and set- theoretic methods in algebra), category theory (module approximations), and algebraic geometry. His work has broad influence on related fields. He has published ninety papers and books until now which appeared in Adv. Math.，Trans. AMS，J. LMS, B. LMS, Math. Z. Forum. Math., J. Algebra, J. Pure and Applied Algebra etc.
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