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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 and on additional set-theoretic hypotheses. For commutative noetherian of Krull dimension , 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 is any ring and there exists a strongly compact cardinal , then the category of all projective modules is -accessible.
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Jan Šaroch, Jan Trlifaj, Test sets for factorization properties of modules. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 217–238DOI 10.4171/RSMUP/66