Research Article
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Year 2020, Volume: 8 Issue: 1, 46 - 50, 20.03.2020

Yusuf Alagöz

https://doi.org/10.36753/mathenot.630031
Cited By: 2

Abstract

References

  • Referans1: J. Clark, C. Lomp, N. Vanaja, and R.Wisbauer, Lifting modules,Frontiers in Mathematics, Birkhaauser Verlag, Basel, 2006.
  • Referans2: E. E. Enochs and O. M. G. Jenda, Relative homological algebra, Berlin: Walter de Gruyter, 2000.
  • Referans3: E. E. Enochs, O. M. G. Jenda, and J. A. Lopez-Ramos, The existence of Gorenstein flat covers, Math. Scand. 94(1) (2004), 46-62.
  • Referans4: P. C. Eklof and J. Trlifaj, How to make Ext vanish, Bull. London Math. Soc. 33(1) (2001), no. 12, 41-51.
  • Referans5: J. R. Garcia Rozas and B. Torrecillas, Relative injective covers, Comm. Algebra 22(8) (1994), 2925-2940.
  • Referans6: C. Megibben, Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155-158.
  • Referans7: A. Moradzadeh-Dehkordi and S. H. Shojaee, Rings in which every ideal is pure-projective or FP-projective, J.Algebra 478 (2017), 419-436.
  • Referans8: V. S. Ramamurthi, On the injectivity and flatness of certain cyclic modules, Proc. Amer. Math. Soc. 48 (1975), 21-25.
  • Referans9: P. F. Smith, Injective modules and prime ideals, Comm. Algebra 9(9) (1981), 989-999.
  • Referans10: M. Y. Wang, Frobenius structure in algebra (chinese),Science Press, Beijing, 2005.
  • Referans11: M. Y. Wang and G. Zhao, On maximal injectivity, Acta Math. Sin. 21(6) (2005), 1451-1458.
  • Referans12: Y. Xiang, Max-injective, max-flat modules and max-coherent rings, Bull. Korean Math. Soc. 47(3), 2010, 611-622.

On M-injective and M-projective Modules

Year 2020, Volume: 8 Issue: 1, 46 - 50, 20.03.2020

Yusuf Alagöz

https://doi.org/10.36753/mathenot.630031
Cited By: 2

Abstract

In
this study, the concept of m-projective modules is introduced. A right R-module
M is said to be m-projective if Ext(M,N)=0 for any m-injective right R-module
N. We prove that every right R-module has a special m-projective precover and
m-injective preenvelope. We characterize C-rings, SF-rings and max-hereditary
rings using m-projective and m-injective modules. 

Keywords

m-injective modules; m-projective modules; max-hereditary rings.

References

  • Referans1: J. Clark, C. Lomp, N. Vanaja, and R.Wisbauer, Lifting modules,Frontiers in Mathematics, Birkhaauser Verlag, Basel, 2006.
  • Referans2: E. E. Enochs and O. M. G. Jenda, Relative homological algebra, Berlin: Walter de Gruyter, 2000.
  • Referans3: E. E. Enochs, O. M. G. Jenda, and J. A. Lopez-Ramos, The existence of Gorenstein flat covers, Math. Scand. 94(1) (2004), 46-62.
  • Referans4: P. C. Eklof and J. Trlifaj, How to make Ext vanish, Bull. London Math. Soc. 33(1) (2001), no. 12, 41-51.
  • Referans5: J. R. Garcia Rozas and B. Torrecillas, Relative injective covers, Comm. Algebra 22(8) (1994), 2925-2940.
  • Referans6: C. Megibben, Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155-158.
  • Referans7: A. Moradzadeh-Dehkordi and S. H. Shojaee, Rings in which every ideal is pure-projective or FP-projective, J.Algebra 478 (2017), 419-436.
  • Referans8: V. S. Ramamurthi, On the injectivity and flatness of certain cyclic modules, Proc. Amer. Math. Soc. 48 (1975), 21-25.
  • Referans9: P. F. Smith, Injective modules and prime ideals, Comm. Algebra 9(9) (1981), 989-999.
  • Referans10: M. Y. Wang, Frobenius structure in algebra (chinese),Science Press, Beijing, 2005.
  • Referans11: M. Y. Wang and G. Zhao, On maximal injectivity, Acta Math. Sin. 21(6) (2005), 1451-1458.
  • Referans12: Y. Xiang, Max-injective, max-flat modules and max-coherent rings, Bull. Korean Math. Soc. 47(3), 2010, 611-622.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Yusuf Alagöz 0000-0002-2535-4679

Submission Date October 7, 2019
Acceptance Date October 21, 2019
Publication Date March 20, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Alagöz, Y. (2020). On M-injective and M-projective Modules. Mathematical Sciences and Applications E-Notes, 8(1), 46-50. https://doi.org/10.36753/mathenot.630031
AMA Alagöz Y. On M-injective and M-projective Modules. Math. Sci. Appl. E-Notes. March 2020;8(1):46-50. doi:10.36753/mathenot.630031
Chicago Alagöz, Yusuf. “On M-Injective and M-Projective Modules”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 46-50. https://doi.org/10.36753/mathenot.630031.
EndNote Alagöz Y (March 1, 2020) On M-injective and M-projective Modules. Mathematical Sciences and Applications E-Notes 8 1 46–50.
IEEE Y. Alagöz, “On M-injective and M-projective Modules”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 46–50, 2020, doi: 10.36753/mathenot.630031.
ISNAD Alagöz, Yusuf. “On M-Injective and M-Projective Modules”. Mathematical Sciences and Applications E-Notes 8/1 (March2020), 46-50. https://doi.org/10.36753/mathenot.630031.
JAMA Alagöz Y. On M-injective and M-projective Modules. Math. Sci. Appl. E-Notes. 2020;8:46–50.
MLA Alagöz, Yusuf. “On M-Injective and M-Projective Modules”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 46-50, doi:10.36753/mathenot.630031.
Vancouver Alagöz Y. On M-injective and M-projective Modules. Math. Sci. Appl. E-Notes. 2020;8(1):46-50.

Cited By

On MF-projective modules
Hacettepe Journal of Mathematics and Statistics
https://doi.org/10.15672/hujms.731098
On max-flat and max-cotorsion modules
Applicable Algebra in Engineering, Communication and Computing
https://doi.org/10.1007/s00200-020-00482-4

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