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arXiv · 1912.03749

Test sets for factorization properties of modules

Jan Šaroch·Jan Trlifaj
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Abstract

Baer's Criterion of injectivity implies that injectivity of a module is a factorization property w.r.t. a single monomorphism. Using the notion of a cotorsion pair, we study generalizations and dualizations of factorization properties in dependence on the algebraic structure of the underlying ring $R$ and on additional set-theoretic hypotheses. For $R$ commutative noetherian of Krull dimension $0 < d < \infty$, we show that the assertion `projectivity is a factorization property w.r.t. a single epimorphism' is independent of ZFC + GCH. We also show that if $R$ is any ring and there exists a strongly compact cardinal $κ> |R|$, then the category of all projective modules is accessible.

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Jan Šaroch, Jan Trlifaj. 2019-12-08. Test sets for factorization properties of modules. https://arxiv.org/abs/1912.03749

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