Affiliation:
1. Department of Algebra , Faculty of Mathematics and Physics , Charles University , Sokolovská 83, 186 75 Prague 8 , Czech Republic
Abstract
Abstract
Baer’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.
Funder
Grantová Agentura České Republiky
Subject
Applied Mathematics,General Mathematics
Cited by
5 articles.
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2. Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings;Journal of Algebra;2022-07
3. Rings whose nonsingular right modules are $R$-projective;Commentationes Mathematicae Universitatis Carolinae;2022-03-02
4. Test sets for factorization properties of modules;Rendiconti del Seminario Matematico della Università di Padova;2020-12-10
5. Max-projective modules;Journal of Algebra and Its Applications;2020-05-07