Dedekind N-group and uniform N-group in near-rings

Document Type : Research Paper

Authors

1 Department of mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

2 Department of Mathematics, University of Nobonyad, Sirjan, Iran

Abstract

In this paper the authors have defined Dedekind $N$-groups, prime $N$-groups, uniform $N$-groups in near rings and have found the relationship between them. For example they have showed the notions uniform $N$-group and Dedekind $N$-group in near rings are equivalent.

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References

[1] E. Khodadadpour and T. Roodbarylor,Valuation near rings, Journal of algebra and related topics, (2) 9 (2021), 95–100.
[2] M. Khoramdel and S. Dolati Pish Hesari, Some notes on dedekind modules, Hacettepe Journal of Mathematics and Statistics, 5 (2011), 627–634.
[3] G. Pilz, Near-Rings, North Holland, Amsterdam, (1983).
[4] M. G. Rinaldi, On the near rings whose proper ideas are prime, San Benedetto del toronto, (1981), 197–200.
[5] M. Sadeghi gougheri and T. Roodbarylor, The construction of fraction N-subgroups in near rings, Italean Journal of pure and applied mathematics, 46 (2021), 272-282.
[6] S. Yamamuro, A note on near rings of mapping, J. Austral. Math. soc., 16 (1973).
Journal of Algebra and Related Topics
Volume 13, Issue 1
July 2025
Pages 61-72

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