Skip to main content
SpringerLink
Log in

3-absorbing ideals and submodules over noncommutative rings

  • Original Paper
  • Published:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Aims and scope Submit manuscript

Abstract

Let R be a noncommutative ring with identity. This paper mainly defines the concept of a 3-absorbing ideal and submodule. It shows that in the case where the ring is commutative, then these notions concide with the one defined by Badawi and Darani. Further, we give an example to show that in general these notions are different and present some properties of 3-absorbing ideals and submodules.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Badawi, A.: On 2-absorbing ideals of commutative rings. Bull. Aust. Math. Soc. 75, 417–429 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Bahphang, A.M., Rege, M.B.: Semi-commutative modules and Armendariz modules. Arab J. Math. Sci. 8(1), 53–65 (2002)

    MathSciNet  MATH  Google Scholar 

  • Darani, A.Y., Soheilnia, F.: 2-Absorbing and weakly 2-absorbing submodules. Thai J. Math. 9(3), 577–584 (2011)

    MathSciNet  MATH  Google Scholar 

  • Dauns, J.: Prime modules. J. Reine Angew, Math. 298, 156–181 (1978)

    MathSciNet  MATH  Google Scholar 

  • Groenewald, N.J.: On \(2\)-absorbing ideals of noncommutative rings, Department of Mathematics and Applied Mathematics, Nelson Mandela University (2018)

  • Groenewald, N.J., Nguyen, B.T.: On \(2\)-absorbing modules over noncommutative rings, 25(2019), 212-223 (2019)

  • Groenewald, N.J., Ssevviiri, D.: Complete prime submodules. Int. Electron. J. Algebra 13, 1–14 (2013)

    MathSciNet  MATH  Google Scholar 

  • Lam, T.Y.: A first course in noncommutative rings, Department of Mathematics, University of California, Springer, New York, Inc., ISBN 0-387-97523-3 (1991)

  • Payrovi, S.H., Babaei, S.: On \(2\)-absorbing submodules. Algebra Colloq. 19, 913–920 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Payrovi, S.H., Babaei, S.: On the \(2\)-absorbing submodules. Iran. J. Math. Sei. Inform. 10(1), 131–137 (2015)

    MathSciNet  MATH  Google Scholar 

  • Pola, E.N., Kianpi, M., Diékouam, L.E.F.: \(n\)-Absorbing submodules and multiplicative modules over valuation rings. Southeast Asian Bull. Math. 43(6), 867–881 (2019)

    MathSciNet  MATH  Google Scholar 

  • Sands, A.D.: Prime ideals in matrix rings. Glasgow Math. J. 2(4), 193–195 (1956)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Higher Teachers’ Training College, University of Maroua, Maroua, Cameroon

    Momo Nizegha Kelie Marline & Diékouam Fotso Luc Eméry

  2. Mathematics Department, Faculty of Sciences, University of Yaounde 1, Yaoundé, Cameroon

    Kianpi Maurice

Authors
  1. Momo Nizegha Kelie Marline
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diékouam Fotso Luc Eméry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kianpi Maurice
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Diékouam Fotso Luc Eméry.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marline, M.N.K., Eméry, D.F.L. & Maurice, K. 3-absorbing ideals and submodules over noncommutative rings. Beitr Algebra Geom (2023). https://doi.org/10.1007/s13366-023-00704-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13366-023-00704-z

Keywords

Mathematics Subject Classification

Search

Navigation