### Jan Šaroch

Charles University, Prague, Czechia### Jan Trlifaj

Charles University, Prague, Czechia

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## Abstract

Baer's Criterion of injectivity implies that injectivity of a module is a factorization property with respect to\ 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 with respect to a single epimorphism' is independent of ZFC + GCH. We also show that if $R$ is any ring and there exists a strongly compact cardinal $\kappa > |R|$, then the category of all projective modules is $\kappa$-accessible.

## Cite this article

Jan Šaroch, Jan Trlifaj, Test sets for factorization properties of modules. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 217–238

DOI 10.4171/RSMUP/66