Research Article
PDF EndNote BibTex RIS Cite

A Note On E-Injective Modules

Year 2022, Volume 26, Issue 6, 1262 - 1266, 31.12.2022
https://doi.org/10.16984/saufenbilder.1094262

Abstract

Let 𝑅 be a commutative ring with identity, 𝑀 an 𝑅-module and 𝐸 a torsion-free 𝑅-module. A submodule 𝑁 of 𝑀 is said to be essential (large) in 𝑀 if the intersection of 𝑁 with each nonzero submodule of 𝑀 is nonzero, that is, 𝑁 ∩ 𝑅𝑚 ≠ 0 for any nonzero element 𝑚 ∈ 𝑀 and we write 𝑁 ≤𝑒 𝑀. It is clear that the class of 𝑒 − 𝑒𝑥𝑎𝑐𝑡 sequences is larger than the class of 𝑒𝑥𝑎𝑐𝑡 sequences. In this study we present the concept of e-injective modules as a generalization of injective modules. The main goal is to give a characterization of e-injective modules in terms of contravariant functor 𝐻𝑜𝑚(−,𝐸)

References

  • [1] I. Akray, A. Zebari, “Essential exact sequences,” Communications of the Korean Mathematical Society, 2020; 35(2):469-480.
  • [2] A. Tercan, C. C. Yücel, “Module Theory, Extending Modules and Generalizations,” Bassel: Birkhäuser, Springer, 2016.
  • [3] J. J. Rotman, J. J. Rotman, “An introduction to homological algebra,” New York: Springer, 2009.

Year 2022, Volume 26, Issue 6, 1262 - 1266, 31.12.2022
https://doi.org/10.16984/saufenbilder.1094262

Abstract

References

  • [1] I. Akray, A. Zebari, “Essential exact sequences,” Communications of the Korean Mathematical Society, 2020; 35(2):469-480.
  • [2] A. Tercan, C. C. Yücel, “Module Theory, Extending Modules and Generalizations,” Bassel: Birkhäuser, Springer, 2016.
  • [3] J. J. Rotman, J. J. Rotman, “An introduction to homological algebra,” New York: Springer, 2009.

Details

Primary Language English
Subjects Mathematics
Journal Section Research Articles
Authors

Abuzer GÜNDÜZ> (Primary Author)
SAKARYA ÜNİVERSİTESİ
0000-0003-3351-2443
Türkiye


Osama NAJİ>
SAKARYA ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ, MATEMATİK BÖLÜMÜ, MATEMATİK PR.
0000-0002-6498-7620
Türkiye

Publication Date December 31, 2022
Submission Date March 28, 2022
Acceptance Date October 22, 2022
Published in Issue Year 2022, Volume 26, Issue 6

Cite

Bibtex @research article { saufenbilder1094262, journal = {Sakarya University Journal of Science}, eissn = {2147-835X}, address = {}, publisher = {Sakarya University}, year = {2022}, volume = {26}, number = {6}, pages = {1262 - 1266}, doi = {10.16984/saufenbilder.1094262}, title = {A Note On E-Injective Modules}, key = {cite}, author = {Gündüz, Abuzer and Naji, Osama} }
APA Gündüz, A. & Naji, O. (2022). A Note On E-Injective Modules . Sakarya University Journal of Science , 26 (6) , 1262-1266 . DOI: 10.16984/saufenbilder.1094262
MLA Gündüz, A. , Naji, O. "A Note On E-Injective Modules" . Sakarya University Journal of Science 26 (2022 ): 1262-1266 <https://dergipark.org.tr/en/pub/saufenbilder/issue/74051/1094262>
Chicago Gündüz, A. , Naji, O. "A Note On E-Injective Modules". Sakarya University Journal of Science 26 (2022 ): 1262-1266
RIS TY - JOUR T1 - A Note On E-Injective Modules AU - AbuzerGündüz, OsamaNaji Y1 - 2022 PY - 2022 N1 - doi: 10.16984/saufenbilder.1094262 DO - 10.16984/saufenbilder.1094262 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1262 EP - 1266 VL - 26 IS - 6 SN - -2147-835X M3 - doi: 10.16984/saufenbilder.1094262 UR - https://doi.org/10.16984/saufenbilder.1094262 Y2 - 2022 ER -
EndNote %0 Sakarya University Journal of Science A Note On E-Injective Modules %A Abuzer Gündüz , Osama Naji %T A Note On E-Injective Modules %D 2022 %J Sakarya University Journal of Science %P -2147-835X %V 26 %N 6 %R doi: 10.16984/saufenbilder.1094262 %U 10.16984/saufenbilder.1094262
ISNAD Gündüz, Abuzer , Naji, Osama . "A Note On E-Injective Modules". Sakarya University Journal of Science 26 / 6 (December 2022): 1262-1266 . https://doi.org/10.16984/saufenbilder.1094262
AMA Gündüz A. , Naji O. A Note On E-Injective Modules. SAUJS. 2022; 26(6): 1262-1266.
Vancouver Gündüz A. , Naji O. A Note On E-Injective Modules. Sakarya University Journal of Science. 2022; 26(6): 1262-1266.
IEEE A. Gündüz and O. Naji , "A Note On E-Injective Modules", Sakarya University Journal of Science, vol. 26, no. 6, pp. 1262-1266, Dec. 2022, doi:10.16984/saufenbilder.1094262

Sakarya University Journal of Science (SAUJS)