Test sets for factorization properties of modules (Q2039356)

Summary: 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.