The Dual Baer Criterion for non-perfect rings

The Dual Baer Criterion for non-perfect rings AbstractBaer’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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

The Dual Baer Criterion for non-perfect rings

Forum Mathematicum, Volume 32 (3): 10 – May 1, 2020

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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2019-0028
Publisher site
See Article on Publisher Site

Abstract

AbstractBaer’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.

Journal

Forum Mathematicumde Gruyter

Published: May 1, 2020

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