Maximal and minimal prime ideals in a near ring
*Muna Sh. G. ShnainCorresponding authorm1u9n7a5@gmail.comDepartment of MathematicsCollege of Education for Pure ScienceUniversity of BabylonBabylon, IraqView full profile → , Ameer A. J. Al-Swidiameer.alswidi@yahoo.comDepartment of MathematicsCollege of Education for Pure ScienceUniversity of BabylonBabylon, Iraq0000-0002-8560-2072View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 May 2025
- Published Online:
- 22 May 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2378
- Pages:
- 1977–1983
Abstract
Keywords
Subject Classifications
References
[1] G. Pilz, Near Rings: The Theory and Its Applications, North-Holland Mathematics Studies, vol. 23. Amsterdam, The Netherlands; New York, USA: North-Holland Publishing Co./Elsevier Science, (1983).
[2] F. Kasch, Modules and Rings, London Mathematical Society Monographs, vol. 17. London, U.K.; New York, USA: Academic Press, (1982).
[3] N. J. Groenewald, “The completely prime radical in near rings,” Acta Mathematica Hungarica, vol. 51, no. 3–4, pp. 301–305 (1988).
[4] D. D. Anderson and E. Smith, “Weakly prime ideals,” Houston Journal of Mathematics, vol. 29, no. 4, p. 831 (1997).
[5] G. Birkenmeier, H. Heatherly, and E. Lee, “Prime ideals in near rings,” Results Math., vol. 24, no. 1, pp. 27–48 (1993).
[6] H. E. Bell, “Near rings in which each element is a power of itself,” Bull. Aust. Math. Soc., vol. 2, no. 3, pp. 363–368 (1970).
[7] A. A. J. Al-Swidi and A. A. Omran, “Uniquely colorable completely equiprime graph of a near ring,” AIP Conference Proceedings, vol. 2845, no. 1, p. 050045 (Sep. 2023), doi: 10.1063/5.0157185.
[8] M. E. Hellman, “The mathematics of public-key cryptography,” Sci. Am., vol. 241, no. 2, pp. 146–157 (1979).
[9] A. A. J. Al-Swidi and A. A. Omran, “Completely equiprime graph of a near ring,” AIP Conference Proceedings, vol. 2475, no. 1, p. 080011 (Mar. 2023), doi: 10.1063/5.0102632.
[10] A. A. Al-Alawani and A. A. J. Al-Swidi, “Union of subgraphs with respect to some ideals on near rings,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 2, pp. 1903–1910 (2025).
[11] M. Bhargava, “Groups as unions of proper subgroups,” The American Mathematical Monthly, vol. 116, no. 5, pp. 413–422 (1959).
[12] A. M. Almamoori, D. Z. Al-Swefee, and M. M. Alzuhery, “Biodegradation of Two Textile Dyes by Bacillus Subtilis,” Asian Journal of Water, Environment and Pollution, vol. 21, no. 3, pp. 71–76 (2024).
[13] H. Q. Raheem, T. S. Al-meamar, and A. M. Almamoori, “Antibiotic profile and antibacterial activity of copper oxide nanoparticles against Pseudomonas fluorescens isolated from wound infection,” Journal of Drug Delivery Technology, vol. 39, no. 3, pp. 383–385 (2019).
