Teori Gelanggang

Tahun Akademik:
Genap 2022/2023
Kelas-Offr:
AL-AL
Deskripsi:
Gelanggang bersih dan turunannya (gelanggang bersih kuat , gelanggang bersih lemah, gelanggang nil-bersih, dan lain-lain); Gelanggang Valuasi dan turunannya (gelanggang valuasi Dubrovin) ; Graph terkait dengan gelanggang (graph pembagi nol, graph nil-bersih, graph pembagi nil-bersih).
Capaian Pembelajaran
  • 1. Mampu membuktikan keterkaitan antar beberapa jenis gelanggang
  • 2. Mampu mengaitkan konsep gelanggang dengan konsep graph
Daftar Pustaka:
  • Lam, T.Y. 2001. A First Course in Noncommutative Rings. Springer-Verlag. New Yorc, Inc.
  • I. F. Ambarsari, S. Irawati, I M. Sulandra, H. Susanto and H. Marubayashi. 2019. Cleanness of a Dubrovin Valuation Ring. AIP Conference Proceedings, 2192, 040001, https://doi.org/10.1063/1.5139127
  • MFMA Habibi, S Irawati, H Susanto, IM Sulandra, H Marubayashi, Angelina Chin Yan Mui. Sufficient conditions for a Dubrovin valuation ring of a simple artinian ring to be nil-clean. AIP Conference Proceedings 2192, 040003 (2019); https://doi.org/10.1063/1.5139129
  • Artikel-artikel terkait pada jurnal internasional bereputasi, terkini, dan relevan
  • Rowen, Louis, H. 1988. Ring Theory. Academic Press, Inc
  • Rangkuman Ring theory http://www.maths.qmul.ac.uk/~rab/MAS305/algnotes10.pdf ; https://www.saylor.org/site/wp-content/uploads/2011/04/Ring- mathematics.pdf http://www1.spms.ntu.edu.sg/~frederique/chap2.pdf
  • Zhao Yicai, 1997. On The Intersection Property of Dubrovin Valuation Rings. https://www.researchgate.net/publication/ 265288697_On_the_intersection_property_of_Dubrovin_valuation_rings
  • David F. Anderson and Philip S. Livingston, 1998. The Zero-Divisor Graph of a Commutative Ring. https://www.researchgate.net/ publication/226466409_Zero-divisor_graphs_in _commutative_rings
  • Ajay Sharma and Dhiren Kumar Basnet. Nil Clean Divisor Graph. https://www.researchgate.net/publication/ 331561768_Nil_Clean_Divisor_Graph
  • Irawati S., H. Marubayashi and A.Ueda, On R-Ideals of a Dubrovin Valuation Ring R (Taylor & Francis, London, 2014), pp. 261-267
  • Irawati S., H. Marubayashi, S. Kobayashi and G. Xie, A Characterization of Fully Bounded Dubrovin Valuation Rings (Scientiae Mathematicae Japonicae Online, 2004), pp. 33-38
  • I. F. Ambarsari, S. Irawati, I M. Sulandra, H. Susanto, A. C. Y. Mui and H. Marubayashi. 2019. The Existence of Clean Elements in a Matrix Ring over Integral Domain and Its Connections with 𝑔(𝑥)-Cleanness and Strongly 𝑔(𝑥)- Cleanness. Journal of Physics: Conference Series, 1397, 012069, https://doi.org/10.1088/1742-6596/1397/1/012069.