2019/12/08 by Šaroch, Jan, Trlifaj, Jan · 1 citation
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1912.03749
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 < ∞, 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.