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Rings and Modules Whose Socles are Relative Ejective

Year 2018, , 1874 - 1877, 01.12.2018
https://doi.org/10.16984/saufenbilder.446955

Abstract

Lifting homomorphism from modules
to modules or even from certain submodule to the modules have been important
both in ring and module theory. In this note we study rings and modules whose
socles are relative ejective. Moreover we reduce our consideration to rings and
modules with injective socles which provides the dual notion to PS
modules.

References

  • E. Akalan, G. F. Birkenmeier, and A. Tercan, “Goldie extending modules”, Comm. Algebra, vol. 37, no. 2, pp. 663–683, 2009.
  • K. R. Goodearl, Ring Theory, New York: Marcel Dekker, 1976.
  • A. Harmancı and P. F. Smith, “Relative injectivity and modules classes”, Comm. Algebra, vol. 20, no. 9, pp. 2471–2501, 1992.
  • W. K. Nicholson and J. F. Watters, “Rings with projective socle”, Proc. Amer. Math. Soc., vol. 102, no. 3, pp. 443–450, 1988.
  • D. W. Sharpe and P. Vámos, Injective Modules, Cambridge England: Cambridge University Press, 1972.
  • P. F. Smith “On the structure of certain PP–rings”, Math. Z., vol. 166, pp. 147–157, 1979.
  • P. F. Smith and A. Tercan “Generalizations of CS–modules”, Comm. Algebra, vol. 21, no. 6, pp. 1809–1847, 1993.
  • A. Tercan and C. C. Yücel, Module Theory, Extending Modules and Generalizations, Bassel: Birkhäuser–Springer, 2016.
Year 2018, , 1874 - 1877, 01.12.2018
https://doi.org/10.16984/saufenbilder.446955

Abstract

References

  • E. Akalan, G. F. Birkenmeier, and A. Tercan, “Goldie extending modules”, Comm. Algebra, vol. 37, no. 2, pp. 663–683, 2009.
  • K. R. Goodearl, Ring Theory, New York: Marcel Dekker, 1976.
  • A. Harmancı and P. F. Smith, “Relative injectivity and modules classes”, Comm. Algebra, vol. 20, no. 9, pp. 2471–2501, 1992.
  • W. K. Nicholson and J. F. Watters, “Rings with projective socle”, Proc. Amer. Math. Soc., vol. 102, no. 3, pp. 443–450, 1988.
  • D. W. Sharpe and P. Vámos, Injective Modules, Cambridge England: Cambridge University Press, 1972.
  • P. F. Smith “On the structure of certain PP–rings”, Math. Z., vol. 166, pp. 147–157, 1979.
  • P. F. Smith and A. Tercan “Generalizations of CS–modules”, Comm. Algebra, vol. 21, no. 6, pp. 1809–1847, 1993.
  • A. Tercan and C. C. Yücel, Module Theory, Extending Modules and Generalizations, Bassel: Birkhäuser–Springer, 2016.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Nuray Eroğlu 0000-0002-0780-2247

Publication Date December 1, 2018
Submission Date July 23, 2018
Acceptance Date September 27, 2018
Published in Issue Year 2018

Cite

APA Eroğlu, N. (2018). Rings and Modules Whose Socles are Relative Ejective. Sakarya University Journal of Science, 22(6), 1874-1877. https://doi.org/10.16984/saufenbilder.446955
AMA Eroğlu N. Rings and Modules Whose Socles are Relative Ejective. SAUJS. December 2018;22(6):1874-1877. doi:10.16984/saufenbilder.446955
Chicago Eroğlu, Nuray. “Rings and Modules Whose Socles Are Relative Ejective”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1874-77. https://doi.org/10.16984/saufenbilder.446955.
EndNote Eroğlu N (December 1, 2018) Rings and Modules Whose Socles are Relative Ejective. Sakarya University Journal of Science 22 6 1874–1877.
IEEE N. Eroğlu, “Rings and Modules Whose Socles are Relative Ejective”, SAUJS, vol. 22, no. 6, pp. 1874–1877, 2018, doi: 10.16984/saufenbilder.446955.
ISNAD Eroğlu, Nuray. “Rings and Modules Whose Socles Are Relative Ejective”. Sakarya University Journal of Science 22/6 (December 2018), 1874-1877. https://doi.org/10.16984/saufenbilder.446955.
JAMA Eroğlu N. Rings and Modules Whose Socles are Relative Ejective. SAUJS. 2018;22:1874–1877.
MLA Eroğlu, Nuray. “Rings and Modules Whose Socles Are Relative Ejective”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1874-7, doi:10.16984/saufenbilder.446955.
Vancouver Eroğlu N. Rings and Modules Whose Socles are Relative Ejective. SAUJS. 2018;22(6):1874-7.

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