Relative Essential Ideals in N-groups

Authors

  • Tapatee Sahoo Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India
  • Bijan Davvaz Department of Mathematics, Yazd University, Yazd, Iran
  • Harikrishnan Panackal Department of Mathematics, Manipal institute of Technology, Mani- pal Academy of Higher Education, Manipal, Karnataka, India
  • Babushri Srinivas Kedukodi Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India
  • Syam Prasad Kuncham Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India

DOI:

https://doi.org/10.5556/j.tkjm.54.2023.4136

Keywords:

Nearring, N-groups, essential ideal, direct summand, complement

Abstract

Let $G$ be an $N$-group where $N$ is a (right) nearring. We introduce the concept of relative essential ideal (or $N$-subgroup) as a generalization of the concept of essential submodule of a module over a ring or a nearring. We provide suitable examples to distinguish the notions relative essential and essential ideals. We prove the important properties and obtain equivalent conditions for the relative essential ideals (or $N$-subgroups) involving the quotient. Further, we derive results on direct sums, complement ideals of $N$-groups and obtain their properties under homomorphism.

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Published

2021-11-08

How to Cite

Sahoo, T., Davvaz, B., Panackal, H., Kedukodi, B. S., & Kuncham, S. P. (2021). Relative Essential Ideals in N-groups. Tamkang Journal of Mathematics, 54. https://doi.org/10.5556/j.tkjm.54.2023.4136

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Papers