Ideal, Gelanggang Faktor Dari Gelanggang Noether
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Lalu Hasan Ghoffari(1)
Universitas Mataram
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Marena Rahayu Gayatri(2*)
Universitas Mataram
(*) Corresponding Author
Keywords:
Abstract algebra, Noetherian rings
Abstract
Abstract algebra is one of the most interesting sciences in mathematics. Many things are learned in abstract algebra. One of them is the Noetherian rings. A Noetherian ring is a ring that is defined based on a finite ideal set of a ring. The method used is a literature review or also called a literature study, namely research conducted by collecting theories and information related to research with the help of references such as books or scientific journals. One of the theorems formed based on the definition of a Noetherian is that if R is a Noetherian ring, then R[x] is also a Noetherian.
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References
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Fraleigh, J.B. (2014). A First Course in Abstract Algebra (7th ed). United Kingdom: Pearson Education Limited.
Husni, M. N. (2022). Diagonalisasi Operator Linear. UJMC (Unisda Journal of Mathematics and Computer Science), 8(2), 7-14.
Juliana, R., Wardhana, I. G. A. W., and Irwansyah. (2021). Some Characteristics of Cyclic Prime, Weakly Prime and Almost Prime Submodule of Gaussian Integer Modulo Over Integer, AIP Conference Proceedings 2329 (1), 020004
Malik, D.S., Mordeson, J.N., & Sen, M.K. (2007). Introduction to Abstract Algebra. United States of America
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.
Maulana, M. (2023). Ideal Prima Pada Daerah Dedekind Berupa Polinom Faktor Berderajat Satu Dari Ring Bilangan Bulat. FRAKTAL: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA, 3(2), 65-69.
Misuki, W. U., Wardhana, I. G. A. W., & Switrayni, N. W. (2021, March). Some Characteristics of Prime Cyclic Ideal On Gaussian Integer Ring Modulo. In IOP Conference Series: Materials Science and Engineering, Vol. 1115, No. 1, p. 012084.
Roman, S. (2008). Advanced Linear Algebra (3rd Ed). Berlin: Springer.
Sihombing, R., Amir, A. K., & Haryanto, L. SIFAT GELANGGANG NOETHERIAN DAN GELANGGANG PERLUASANNYA.
Switrayni, N. W., Wardhana, I. G. A. W., & Aini, Q. (2022). On Cyclic Decomposition Of Z-Module M_ {m× r}(Z_n). Journal of Fundamental Mathematics and Applications (JFMA), 5(1), 47-51.
Wardhana, I. G. A. W., Astuti, P., & Muchtadi-Alamsyah, I. (2016). On almost prime submodules of a module over a principal ideal domain. JP Journal of Algebra, Number Theory and Applications, 38(2), 121-128.
Wardhana, I. G. A. W., Nghiem, N. D. H., Switrayni, N. W., & Aini, Q. (2021). A note on almost prime submodule of CSM module over principal ideal domain. In Journal of Physics: Conference Series, Vol. 2106, No. 1, p. 012011.
Wardhana, I. G. A. W. W., & Maulana, F. (2021). Sebuah Karakteristik dari Modul Uniserial dan Gelanggang Uniserial. UJMC (Unisda Journal of Mathematics and Computer Science), 7(2), 9-18.
Wardhana, I. G. A. W. (2022). The Decomposition of a Finitely Generated Module over Some Special Ring. JTAM (Jurnal Teori dan Aplikasi Matematika), 6(2), 261-267.
Zhao, K. (2021). Ring and Field Theory. Singapore : World Scientific.
Published
2023-05-04
How to Cite
Ghoffari, L., & Gayatri, M. R. (2023). Ideal, Gelanggang Faktor Dari Gelanggang Noether. FRAKTAL: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA, 4(1), 31-36. https://doi.org/10.35508/fractal.v4i1.9790
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