Gelanggang Prima Lemah Kiri Penuh

Muhammad Nur Hidayat Taufiqurrahman; Dellavitha Nasution

doi:10.15575/kubik.v9i1.33239

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Muhammad Nur Hidayat Taufiqurrahman
Institut Teknologi Bandung
Indonesia

Dellavitha Nasution
Institut Teknologi Bandung
Indonesia

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Gelanggang Prima Lemah Kiri Penuh

Muhammad Nur Hidayat Taufiqurrahman^(1*), Dellavitha Nasution⁽²⁾

(1) Institut Teknologi Bandung, Indonesia
(2) Institut Teknologi Bandung, Indonesia
(*) Corresponding Author

Abstract

Tulisan karya Abouhalaka dan Findik [7] yang berjudul “Almost Prime Ideals in Noncommutative Rings” menghasilkan konsep tentang gelanggang dengan setiap ideal kanannya adalah ideal hampir prima yang disebut dengan gelanggang hampir prima kanan penuh. Paper ini menerapkan konsep tersebut untuk ideal prima lemah kiri, dan akan membuktikan bahwa sifat-sifat pada ideal hampir prima kanan yang diperoleh Abouhalaka dan Findik juga berlaku pada ideal prima lemah kiri dengan suatu kondisi tambahan. Selain itu, penulis memberikan hasil tambahan untuk modul fraksi yang merupakan ideal hampir prima.

Keywords

ideal prima kiri ; ideal prima lemah kiri ; ideal hampir prima kiri ; gelanggang prima lemah kiri penuh ; gelanggang prima lemah kiri hampir penuh.

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References

A. Abouhalaka and Ş. Fındık, “Almost prime ideals in noncommutative rings,” Serdica Mathematical Journal, vol. 48, no. 4, pp. 235–246, 2022, doi: 10.55630/serdica.2022.48.235-246.

Y. Hirano, E. Poon, and H. Tsutsui, “On rings in which every ideal is weakly prime,” Bulletin of the Korean Mathematical Society, vol. 47, no. 5, pp. 1077–1087, 2010, doi: 10.4134/BKMS.2010.47.5.1077.

A. E. Ashour and M. Hamoda, “Characterization of Weakly Primary Ideals over Non-commutative Rings,” International Mathematical Forum, vol. 9, no. 34, pp. 1659–1667, 2014.

W. D. Blair and H. Tsutsui, “Fully prime rings,” Commun Algebra, vol. 22, no. 13, pp. 5389–5400, 1994, doi: 10.1080/00927879408825136.

D. I. C. Mendes, “Fully * -prime rings with involution,” Mathematica Pannonica, vol. 26, no. 2, pp. 119–135, 2018.

D. D. Anderson and M. Bataineh, “Generalizations of prime ideals,” Commun Algebra, vol. 36, no. 2, pp. 686–696, 2008, doi: 10.1080/00927870701724177.

N. Groenewald, “Weakly prime and weakly completely prime ideals of noncommutative rings,” International Electronic Journal of Algebra, vol. 28, no. July, pp. 43–60, 2020, doi: 10.24330/ieja.768127.

S. M. Bhatwadekar and P. K. Sharma, “Unique factorization and birth of almost primes,” Commun Algebra, vol. 33, no. 1, pp. 43–49, 2005, doi: 10.1081/AGB-200034161.

T.-Y. Lam, A First Course in Noncommutative Rings, Second Edi. New York: Springer US, 2001.

M. Shabir, “One-sided Prime Ideals in Semirings,” KYUNGPOOK Math. J, vol. 47, pp. 473–480, 2007.

DOI: https://doi.org/10.15575/kubik.v9i1.33239

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