Geodesic
PURE-INJECTIVITY FROM A DIFFERENT PERSPECTIVE
Glasgow mathematical journal, Tome 60 (2018) no. 1, pp. 135-151

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DOI

The study of pure-injectivity is accessed from an alternative point of view. A module M is called pure-subinjective relative to a module N if for every pure extension K of N, every homomorphism N → M can be extended to a homomorphism K → M. The pure-subinjectivity domain of the module M is defined to be the class of modules N such that M is N-pure-subinjective. Basic properties of the notion of pure-subinjectivity are investigated. We obtain characterizations for various types of rings and modules, including absolutely pure (or, FP-injective) modules, von Neumann regular rings and (pure-) semisimple rings in terms of pure-subinjectivity domains. We also consider cotorsion modules, endomorphism rings of certain modules, and, for a module N, (pure) quotients of N-pure-subinjective modules. 
LÓPEZ-PERMOUTH, S. R.; MASTROMATTEO, J.; TOLOOEI, Y.; UNGOR, B. PURE-INJECTIVITY FROM A DIFFERENT PERSPECTIVE. Glasgow mathematical journal, Tome 60 (2018) no. 1, pp. 135-151. doi: 10.1017/S0017089516000616
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     author = {L\'OPEZ-PERMOUTH, S. R. and MASTROMATTEO, J. and TOLOOEI, Y. and UNGOR, B.},
     title = {PURE-INJECTIVITY {FROM} {A} {DIFFERENT} {PERSPECTIVE}},
     journal = {Glasgow mathematical journal},
     pages = {135--151},
     year = {2018},
     volume = {60},
     number = {1},
     doi = {10.1017/S0017089516000616},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000616/}
}
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%A TOLOOEI, Y.
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