Test sets for factorization properties of modules
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 217-238
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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 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 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 κ>|R|, then the category of all projective modules is κ-accessible.

Publié le :
DOI : 10.4171/rsmup/66
Classification : 16, 03 
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     author = {\v{S}aroch, Jan and Trlifaj, Jan},
     title = {Test sets for factorization properties of modules},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {217--238},
     year = {2020},
     volume = {144},
     doi = {10.4171/rsmup/66},
     mrnumber = {4186456},
     zbl = {1477.16003},
     language = {en},
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}
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Šaroch, Jan; Trlifaj, Jan. Test sets for factorization properties of modules. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 217-238. doi: 10.4171/rsmup/66

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