JournalsrsmupVol. 144pp. 217–238

Test sets for factorization properties of modules

  • 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 RR and on additional set-theoretic hypotheses. For RR commutative noetherian of Krull dimension 0<d<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 RR is any ring and there exists a strongly compact cardinal κ>R\kappa > |R|, then the category of all projective modules is κ\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