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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Alahmadi, A. N., Alkan, M. and López-Permouth, S. R., Poor modules: The opposite of injectivity, Glasgow Math. J. 52 (A) (2010), 7–17. Google Scholar

[2] 2. Al Thani, N. M., Pure Baer injective modules, Internat. J. Math. Math. Sci. 20 (3) (1997), 529–538. Google Scholar

[3] 3. Aydogdu, P. and López-Permouth, S. R., An alternative perspective on injectivity of modules, J. Algebra 338 (1) (2011), 207–219. Google Scholar

[4] 4. Bican, L., El Bashir, R. and Enochs, E., All modules have flat covers, Bull. London Math. Soc. 33 (4) (2001), 385–390. Google Scholar | DOI

[5] 5. Er, N., López-Permouth, S. R. and Sokmez, N., Rings whose modules have maximal and minimal injectivity domains, J. Algebra 330 (1) (2011), 404–417. Google Scholar

[6] 6. Harmanci, A., López-Permouth, S. R. and Ungor, B., On the pure-injectivity profile of a ring, Comm. Algebra 43 (11) (2015), 4984–5002. Google Scholar | DOI

[7] 7. Lam, T. Y., Lectures on modules and rings (Springer-Verlag, New York, 1999). Google Scholar

[8] 8. López-Permouth, S. R. and Simental, J., Characterizing rings in terms of the extent of the injectivity and projectivity of their modules, J. Algebra 362 (2012), 56–69. Google Scholar

[9] 9. Maddox, B. H., Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155–158. Google Scholar | DOI

[10] 10. Prest, M., Pure-injective modules, Arab. J. Sci. Eng. Sect. A Sci. 34 (1D) (2009), 175–191. Google Scholar

[11] 11. Rotman, J. J., An introduction to homological algebra (Academic Press, New York, 1979). Google Scholar

[12] 12. Stenström, B., Coherent rings and FP-injective modules, J. London Math. Soc. 2 (1970), 323–329. Google Scholar

[13] 13. Tuganbaev, A., Rings close to regular, Mathematics and its Applications, 545, Kluwer Academic Publishers, Dordrecht, 2002. Google Scholar

[14] 14. Warfield, R. B. Jr, Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699–719. Google Scholar

[15] 15. Wisbauer, R., Foundations of module and ring theory (Gordon and Breach Science Publishers, Philadelphia, 1991). Google Scholar

[16] 16. Xu, J., Flat covers of modules (Springer-Verlag, Berlin, Heidelberg, 1996). Google Scholar

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