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MATLIS INJECTIVE MODULES

  • Received : 2011.10.15
  • Published : 2013.03.31
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Abstract

In this paper, Matlis injective modules are introduced and studied. It is shown that every R-module has a (special) Matlis injective preenvelope over any ring R and every right R-module has a Matlis injective envelope when R is a right Noetherian ring. Moreover, it is shown that every right R-module has an ${\mathcal{F}}^{{\perp}1}$-envelope when R is a right Noetherian ring and $\mathcal{F}$ is a class of injective right R-modules.

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References

  1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Grad. Texts in Math. 13, Springer-Verlag, New York 1974.
  2. S. Bazzoni, When are definable classes tilting and cotilting classes?, J. Algebra 320 (2008), no. 12, 4281-4299. https://doi.org/10.1016/j.jalgebra.2008.08.028
  3. H. Cartan and S. Eilenberg, Homological Algebra, Princeton Math. Ser., 1956.
  4. P. C. Eklof and S. Shelah, On Whitehead modules, J. Algebra 142 (1991), no. 2, 492-510. https://doi.org/10.1016/0021-8693(91)90321-X
  5. P. C. Eklof and J. Trlifaj, How to make Ext vanish, Bull. Lond. Math. Soc. 23 (2001), no. 1, 41-51.
  6. E. E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math. 39 (1981), no. 3, 189-209. https://doi.org/10.1007/BF02760849
  7. E. E. Enochs and O. M. G. Jenda, Copure injective modules, Quaest. Math. 14 (1991), no. 4, 401-409. https://doi.org/10.1080/16073606.1991.9631658
  8. E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Expos. Math. 30, de Gruyter, Berlin 2000.
  9. A. Facchini, Module Theory: Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules, Progress in Math. vol. 167, Birkhauser, Basel, 1998.
  10. R. Gobel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, de Gruyter Expos. Math. 41, de Gruyter, Berlin 2006.
  11. P. A. Guil Asensio and I. Herzog, Sigma-cotorsion rings, Adv. Math. 191 (2005), no. 1, 11-28. https://doi.org/10.1016/j.aim.2004.01.006
  12. T. Y. Lam, Lectures on Modules and Rings, Grad. Texts in Math. 189, Springer, New York 1999.
  13. J. J. Rotman, An Introduction to Homological Algebra, Pure Appl. Math. 85, Academic Press, New York 1979.

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  1. Relative Projective and Injective Dimensions vol.44, pp.8, 2016, https://doi.org/10.1080/00927872.2015.1065852
  2. Matlis flat modules vol.9, pp.2, 2016, https://doi.org/10.1515/tmj-2016-0023