RADIKAL SUPERNILPOTENT BERTINGKAT

Puguh Wahyu Prasetyo


DOI: https://doi.org/10.14710/jfma.v2i1.25

Abstract


The development of Ring Theory motivates the existence of the development of the Radical Theory of Rings. This condition is motivated since there are rings which have properties other than those owned by the set ring of all integers. These rings are collected so that they fulfill certain properties and they are called radical classes of rings. As the development of science about how to separate the properties of radical classes of rings motivates the existence of supernilpotent radical classes. On the other hand, there exists the concept of graded rings. This concept can be generalized into the Radical Theory of Rings. Thus, the properties of the graded supernilpotent radical classes are very interesting to investigate. In this paper, some graded supernilpotent radical of rings are given and their construction will be described. It follows from this construction that the graded Jacobson radical is a graded supernilpotent radical.


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References


B. Gardner and R. Wiegandt, Radical Theory of Rings, New York: Marcel Dekker, Inc, 2004.

P. W. Prasetyo, Necessary And Sufficient Conditions For U(*_k) To Coincide With The Prime Radical β (Disertasi), Yogyakarta: Universitas Gadjah Mada, 2018.

P. W. Prasetyo, S. Wahyuni, I. E. Wijayanti and H. France-Jackson, "Dari Radikal Ring Ke Radikal Modul (From Radical of Rings To Radical of Modules)," in Prosiding Seminar Nasional Matematika 2014 Universitas Jember, Jember, 2014.

H. Fang and P. Stewart, "Radical Theory for Graded Rings," J. Austral. Math. Soc, vol. 52, pp. 143-153, 1992.


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