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A note On 2-prime ideals | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 263-273 اصل مقاله (486.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.21796.1467 | ||
| نویسندگان | ||
| Somayeh Hadjirezaei* ؛ Vajihe Sharifi | ||
| Department of Mathematics, Vali-e-Asr University, Rafsanjan, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity. In this paper, we study 2-prime ideals of a Dedekind domain and a Pr\"{u}fer domain. We prove that a nonzero ideal $I$ of a Dedekind domain $R$ is 2-prime if and only if $I=P^{\alpha}$, for some maximal ideal $P$ of $R$ and positive integer $\alpha$. We give some results of ring $R$ in which every ideal $I$ is 2-prime. Finally, we define almost 2-prime, almost 2-primary and weakly 2-primary ideals, and investigate some properties of these ideals. | ||
| کلیدواژه‌ها | ||
| 2-prime ideal؛ almost 2-prime ideal؛ almost 2-primary؛ ideal؛ weakly 2-primary ideal | ||
| مراجع | ||
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[1] Anderson, D. D., & Smith, E. (2003). Weakly prime ideals. Houston Journal of Mathematics, 29(4), 831-840. Record Identi er: 9984230419402771
[2] Atani, S. E., & Farzalipour, F. (2005). On weakly primary ideals. https://doi.org/10.1515/GMJ.2005.423
[3] Atiyah, M. F., & Macdonald, I. G. (1969). Introduction to commutative algebra. Addison-Wesley, Reading, Massachusetts.
[4] Badawi, A. (2007). On 2-absorbing ideals of commutative rings. Bulletin of the Australian Mathematical Society, 75(3), pp.417{429. https://doi.org/10.1017/S0004972700039344
[5] Beddani, C., & Messirdi, W. (2016). 2-prime ideals and their applications. Journal of Algebra and Its Applications, 15(03), 1650051. https://doi.org/10.1142/S0219498816500511
[6] Bhatwadekar, S. M., & Sharma, P.K. (2005). Unique factorization and birth of almost primes. Communications in Algebra®, 33(1), pp.43-49. DOI:10.1081/AGB-200034161
[7] Gilmer, R.W. (1962). Rings in which semi-primary ideals are primary. Paci c Journal of Mathematics, 12(4), pp.1273-1276. DOI:10.2140/pjm.1962.12.1273
[8] Larsen, M. D., & McCarthy, P. J. (1971). Multiplicative theory of ideals. AcademicPress, New York.
[9] Mott, J. L. (1963). On Invertible Ideals in a Commutative Ring. Louisiana State University and Agricultural & Mechanical College. https://doi.org/10.31390/gradschool-disstheses.850
[10] Nikandish, R., Nikmehr, M. J., & Yassine, A. (2020). More on the 2-prime ideals of commutative rings. Bulletin of the Korean Mathematical Society, 57(1), 117-126. https://doi.org/10.4134/BKMS.b190094
[11] Sharp, R. Y. (2000). Steps in commutative algebra (No. 51). Cambridge university press. https://doi.org/10.1017/CBO9780511623684
[12] Wang, F., & Kim, H. (2016). Foundations of commutative ring and their modules(Vol. 22). Singapore:Springer.
[13] Wisbauer, R. (2018). Foundations of module and ring theory. Routledge. https://doi.org/10.1201/9780203755532 | ||
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