On Weakly S-2-Absorbing Submodules

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-48
Published: May 22, 2023
Cite as:
Govindarajulu Narayanan Sudharshana, On Weakly S-2-Absorbing Submodules, Int. J. Anal. Appl., 21 (2023), 48.

Main Article Content

Govindarajulu Narayanan Sudharshana

Abstract

Let R be a commutative ring with identity and let M be a unitary R-module. In this paper, we introduce the notion of weakly S-2-absorbing submodule. Suppose that S is a multiplicatively closed subset of R. A submodule P of M with (P:R M)∩S=∅ is said to be a weakly S-2-absorbing submodule if there exists an element s ∈ S such that whenever a,b∈R and m∈M with 0≠abm∈P, then sab∈(P: M) or sam∈P or sbm∈P. We give the characterizations, properties and examples of weakly S-2-absorbing submodules.

Article Details

References

  1. M.M. Ali, Idempotent and Nilpotent Submodules of Multiplication Modules, Commun. Algebra. 36 (2008), 4620–4642. https://doi.org/10.1080/00927870802186805.
  2. M.M. Ali, Residual Submodules of Multiplication Modules, Beitr. Algebra Geom. 46 (2005), 405-422.
  3. F.A.A. Almahdi, E.M. Bouba, M. Tamekkante, On Weakly S-Prime Ideals of Commutative Rings, An. Univ. Ovidius Const. - Ser. Mat. 29 (2021), 173–186. https://doi.org/10.2478/auom-2021-0024.
  4. R. Ameri, On the Prime Submodules of Multiplication Modules, Int. J. Math. Math. Sci. 2003 (2003), 1715–1724. https://doi.org/10.1155/s0161171203202180.
  5. S.E. Atani, F. Farzalipour, On Weakly Prime Submodules, Tamkang J. Math. 38 (2007), 247–252. https://doi.org/10.5556/j.tkjm.38.2007.77.
  6. A.Y. Darani, F. Soheilnia, 2-Absorbing and Weakly 2-Absorbing Submodules, Thai J. Math. 9 (2011), 577-584.
  7. A.Y. Darani, F. Soheilnia, U. Tekir, G. Ulucak, On Weakly 2-Absorbing Primary Submodules of Modules Over Commutative Rings, J. Korean Math. Soc. 54 (2017), 1505–1519. https://doi.org/10.4134/JKMS.J160544.
  8. Z.A. El-Bast, P.P. Smith, Multiplication Modules, Commun. Algebra. 16 (1988), 755-779. https://doi.org/10.1080/00927878808823601.
  9. N.J. Groenewald, On Weakly Prime and Weakly 2-absorbing Modules over Noncommutative Rings, Kyungpook Math. J. 61 (2021), 33–48. https://doi.org/10.5666/KMJ.2021.61.1.33.
  10. A. Hamed, A. Malek, S-prime ideals of a commutative ring, Beitr. Algebra Geom. 61 (2019), 533–542. https://doi.org/10.1007/s13366-019-00476-5.
  11. H.A. Khashan, E.Y. Celikel, On Weakly S-Prime Submodules, (2021). https://doi.org/10.48550/ARXIV.2110.14639.
  12. R.L. McCasland, M.E. Moore, On Radicals of Submodules of Finitely Generated Modules, Can. Math. Bull. 29 (1986), 37–39. https://doi.org/10.4153/CMB-1986-006-7.
  13. S. Moradi, A. Azizi, Weakly 2-Absorbing Submodules of Modules, Turk. J. Math. 40 (2016), 350-364.
  14. E. Sengelen Sevim, T. Arabaci, U. Tekir, On S-prime submodles, Turkish Journal of Mathematics 43.2(2019),1036- 1046.
  15. P.F. Smith, Some Remarks on Multiplication Modules, Arch. Math. 50 (1988), 223–235. https://doi.org/10.1007/BF01187738.
  16. G. Ulucak, Ü. Tekir, S. Koç, On S-2-Absorbing Submodules and Vn-Regular Modules, An. Univ. Ovidius Const. - Ser. Mat. 28 (2020), 239–257. https://doi.org/10.2478/auom-2020-0030.