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ON S-EXTENDING MODULES

Year 2020, , 102 - 113, 07.01.2020
https://doi.org/10.24330/ieja.662972

Abstract

Here we introduce and study the concept of relative superfluous injectivity, which is a generalization of relative injectivity. We show some of the properties that hold true for relative injectivity still hold for relative superfluous injectivity. We also introduce and characterize the new concept of superfluous extending modules. Finally, we make use of relative superfluous injectivity to study direct sums of superfluous extending modules.

References

  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
  • W. D. Burgess and R. Raphael, On modules with the absolute direct summand property, Ring Theory (Granville, OH, 1992), World Sci. Publ., River Edge, NJ, (1993), 137-148.
  • H. Q. Dinh, A note on pseudo injective modules, Comm. Algebra, 33(2) (2005), 361-369.
  • N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbaur, Extending Modules, with the collaboration of John Clark and N. Vanaja, Pitman Research Notes in Mathematics Series, 313, Longman Scienti c & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994.
  • M. A. Kamal and B. J. Muller, Extending modules over commutative domains, Osaka J. Math., 25(3) (1988), 531-538.
  • E. Mermut, C. Santa-Clara and P. F. Smith, Injectivity relative to closed sub- modules, J. Algebra, 321(2) (2009), 548-557.
  • M. Okado, On the decomposition of extending modules, Math. Japon., 29(6) (1984), 939-941.
  • M. F. Yousif and Y. Zhou, FP-injective, simple-injective, and quasi-Frobenius rings, Comm. Algebra, 32(6) (2004), 2273-2285.
Year 2020, , 102 - 113, 07.01.2020
https://doi.org/10.24330/ieja.662972

Abstract

References

  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
  • W. D. Burgess and R. Raphael, On modules with the absolute direct summand property, Ring Theory (Granville, OH, 1992), World Sci. Publ., River Edge, NJ, (1993), 137-148.
  • H. Q. Dinh, A note on pseudo injective modules, Comm. Algebra, 33(2) (2005), 361-369.
  • N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbaur, Extending Modules, with the collaboration of John Clark and N. Vanaja, Pitman Research Notes in Mathematics Series, 313, Longman Scienti c & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994.
  • M. A. Kamal and B. J. Muller, Extending modules over commutative domains, Osaka J. Math., 25(3) (1988), 531-538.
  • E. Mermut, C. Santa-Clara and P. F. Smith, Injectivity relative to closed sub- modules, J. Algebra, 321(2) (2009), 548-557.
  • M. Okado, On the decomposition of extending modules, Math. Japon., 29(6) (1984), 939-941.
  • M. F. Yousif and Y. Zhou, FP-injective, simple-injective, and quasi-Frobenius rings, Comm. Algebra, 32(6) (2004), 2273-2285.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Manar E. Tabarak This is me

M. A. Kamal This is me

M. H. Elbaroudy This is me

Salah El Din S. Hussien This is me

Publication Date January 7, 2020
Published in Issue Year 2020

Cite

APA Tabarak, M. E., Kamal, M. A., Elbaroudy, M. H., Hussien, S. E. D. S. (2020). ON S-EXTENDING MODULES. International Electronic Journal of Algebra, 27(27), 102-113. https://doi.org/10.24330/ieja.662972
AMA Tabarak ME, Kamal MA, Elbaroudy MH, Hussien SEDS. ON S-EXTENDING MODULES. IEJA. January 2020;27(27):102-113. doi:10.24330/ieja.662972
Chicago Tabarak, Manar E., M. A. Kamal, M. H. Elbaroudy, and Salah El Din S. Hussien. “ON S-EXTENDING MODULES”. International Electronic Journal of Algebra 27, no. 27 (January 2020): 102-13. https://doi.org/10.24330/ieja.662972.
EndNote Tabarak ME, Kamal MA, Elbaroudy MH, Hussien SEDS (January 1, 2020) ON S-EXTENDING MODULES. International Electronic Journal of Algebra 27 27 102–113.
IEEE M. E. Tabarak, M. A. Kamal, M. H. Elbaroudy, and S. E. D. S. Hussien, “ON S-EXTENDING MODULES”, IEJA, vol. 27, no. 27, pp. 102–113, 2020, doi: 10.24330/ieja.662972.
ISNAD Tabarak, Manar E. et al. “ON S-EXTENDING MODULES”. International Electronic Journal of Algebra 27/27 (January 2020), 102-113. https://doi.org/10.24330/ieja.662972.
JAMA Tabarak ME, Kamal MA, Elbaroudy MH, Hussien SEDS. ON S-EXTENDING MODULES. IEJA. 2020;27:102–113.
MLA Tabarak, Manar E. et al. “ON S-EXTENDING MODULES”. International Electronic Journal of Algebra, vol. 27, no. 27, 2020, pp. 102-13, doi:10.24330/ieja.662972.
Vancouver Tabarak ME, Kamal MA, Elbaroudy MH, Hussien SEDS. ON S-EXTENDING MODULES. IEJA. 2020;27(27):102-13.