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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2024 / Volume: 73 Issue: 4

Ideal theory of $(m, n)$-near rings

Fahime Mohammadi(Yazd University)0009-0003-1562-9231
Bijan Davvaz(Yazd University)0000-0003-1941-5372
Pages
—
Publication Date
2024-12-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We describe the concept of homomorphisms between $ (m, n) $-near rings that preserve the $(m, n)$-near ring structure, and give some results in this respect.

📌 3 Key Takeaways

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Objective & Hypothesis:The aim of this research work is to define and characterize a new class of $n$-ary algebras that we call $(m,n)$-near rings.
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Key Findings & Data:We investigate the notions of $i$-$R$-groups, $i$-$(m, n) $-near field, prime ideals, primary ideals and subtractive ideals of $(m,n)$-near rings.
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Conclusion & Impact:We describe the concept of homomorphisms between $ (m, n) $-near rings that preserve the $(m, n)$-near ring structure, and give some results in this respect.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:n)-near ring · n)-near field · ideal

Abstract

The aim of this research work is to define and characterize a new class of $n$-ary algebras that we call $(m,n)$-near rings. We investigate the notions of $i$-$R$-groups, $i$-$(m, n) $-near field, prime ideals, primary ideals and subtractive ideals of $(m,n)$-near rings. We describe the concept of homomorphisms between $ (m, n) $-near rings that preserve the $(m, n)$-near ring structure, and give some results in this respect.

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Cite This Article

Mohammadi, F., Davvaz, B. (2024). Ideal theory of $(m, n)$-near rings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 4. https://doi.org/10.31801/cfsuasmas.1494749

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References (14)

  1. Alam, S., Rao, S., Davvaz, B., (m, n)-Semirings and a generalized fault- tolerance algebra of systems, J. Appl. Math., (2013), Art. ID 482391, 10 pp. https://doi.org/10.1155/2013/482391
  2. Balakrishnan, R., Chelvam, T., $\alpha_{1}$, $\alpha_{2}$,-Near-rings, International Journal of Algebra, 4(2) (2010), 71–79.
  3. Chaudhari, J. N., Nemade, H., Davvaz, B., On partitioning ideals of (m, n)-semirings, Asian European Journal of Mathematics, 15(8) (2022), 2250144 (13 pages). https://doi.org/10.1142/S1793557122501443
  4. Clay, J., Near-rings: Geneses and Applications, Oxford, New York, 1992. https://doi.org/10.1093/oso/9780198533986.002.0001
  5. Crombez, G., On (m, n)-rings, Abh. Math. Semin. Univ. Hambg., 37 (1972), 180–199. https://doi.org/10.1007/BF02999695
  6. Crombez, G., Timm, J., On (n, m)-quotient rings, Abh. Math. Semin. Univ. Hambg., 37 (1972), 200–203. https://doi.org/10.1007/BF02999696
  7. Davvaz, B., Leoreanu-Fotea, V., Vougiouklis, T., A survey on the theory of n-hypergroups, Mathematics, 11 (2023), 551. https://doi.org/10.3390/math11030551
  8. Davvaz, B., Mohammadi, F., Different types of ideals and homomorphisms of (m, n)- semirings, TWMS J. Pure Appl. Math., 12(2) (2021), 209-222.
  9. Dickson, L., Definitions of a group and a field by independent postulates, Trans. Amer. Math. Soc., 6 (1905), 198-204.
  10. Dörnte, W., Untersuchungen uber einen verallgemeinerten Gruppenbegriff, Math. Z., 29 (1929), 1-19.
  11. Dudek, W. A., Glazek, K., Around the Hosszu-Gluskin theorem for n-ary groups, Discret. Math., 308 (2008), 4861-4876. https://doi.org/10.1016/j.disc.2007.09.005
  12. Post, E. L., Polyadic groups, Trans. Amer. Math. Soc., 48 (1940), 208-350.
  13. Usan, J., Zizovic, M., Some remarks on (m, n)-rings, Filomat, 13 (1999), 53-57.
  14. Vasantha Kandasamy, W. B., Smarandache near-rings, American Research Press Rehoboth, NM, 2002.