Prime ideal on the end_Z (Z^n ) Ring

Zakaria Bani Ikhtiyar, Nikken Prima Puspita, Titi Udjiani

Abstract


The set of all endomorphisms over -module  is a non-empty set denoted by . From  we can construct the ring of  over addition and composition function. The prime ideal is an ideal which satisfies the properties like the prime numbers. In this paper, we take the ring of integer number  and the module of  over  such that the  is a ring. Furthermore, we show the existences of prime ideal on the . We also applied a prime ideal property to prime ideal on   .


Keywords


Endomorphism; Endomorphism Ring; Ideal; Module; Prime Ideal.

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References


Adkins, W. A., & Weintraub, S. H. (1992). Algebra : An Approach via module theory. Springer-Verlag.

Davvaz, B. (2006). (∈,∈∨ q)-fuzzy subnear-rings and ideals. Soft Computing, 10(3), 206-211.

Dummit, D. S., & Foote, R. M. (2004). Abstract algebra (3rd ed.). John Wiley & Sons.

Fraleigh J B. (1999). A first course in abstract algebra. Addison Wesley Publishing Company.

Gallian, J. A. (2017). Contemporary abstract algebra (9th ed.). Cengange Learning.

Groenewald N. (2020). Weakly prime and weakly completely prime ideals of noncommutative rings. International Electronic Journal of Algebra, 28, 43-60.

Herstein I.N. (1975). Topics in algebra (2nd ed.). John Wiley & Sons.

Jensen, C. U., & Lenzing, H. (1989). Model theoretic algebra with particular emphasis on fields, rings, modules (Vol. 2). CRC Press.

Jianming, Z., & Xueling, M. (2004). Intuitionistic fuzzy ideals of near-rings. Scientae Math Japonicae, 61(2), 219-223.

Khairunnisa, Y., & Wardhana, I. G. A. W. (2019). Sifat-sifat ideal prima pada gelanggang noether. 3rd ELPSA Conference, 60–64.

Khariani, Q., Amir, K. A., & Erawaty, N. (2014). Ideal prima dan ideal maksimal pada gelanggang polinomial. Jurnal Matematika, Statistika, & Komputasi, 11(1), 71–76.

Kleiner, I. (1998). From numbers to rings: The early history of ring theory. Elemente Der Mathematik, 53, 18–35.

Koh K. (1971). On one sided ideals of a prime type. Proceeding of the American Mathematical Society, 28(2), 321-329.

Lindo, H. (2017). Trace ideals and centers of endomorphism rings of modules over commutative rings. Journal of Algebra, 482, 102-130.

Marks, G. (2002). Reversible and symmetric rings. Journal of Pure and Applied Algebra, 174(3), 311-318.

Matlis, E. (1958). Injective modules over Noetherian rings. Pacific Journal of Mathematics, 8(3), 511-528.

Maulana, F., Wardhana, I. G. A. W., & Switrayni, N. W. (2019). Ekivalensi ideal hampir prima dan ideal prima pada bilangan bulat gauss. Eigen Mathematics Journal, 2(1), 1–5.

McCoy, N. H. (1949). Prime ideals in general rings. American Journal of Mathematics, 71(4), 823–833.

Nicholson, W. K. (1976). Semiregular modules and rings. Canadian Journal of Mathematics, 28(5), 1105-1120.

Nobusawa, N. (1964). On a generalization of the ring theory. Osaka Journal of Mathematics, 1(1), 81-89.

Volodin, I. A. (1971). Algebraic K-theory as extraordinary homology theory on the category of associative rings with unity. Mathematics of the USSR-Izvestiya, 5(4), 859.

Wahyuni, S., Wijayanti, I. E., Yuwaningsih, D. A., & Hartanto, A. D. (2016). Teori ring dan modul. Gadjah Mada University Press.




DOI: http://dx.doi.org/10.24042/ajpm.v13i2.13193

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