A. Mu'In, S. Irawati, H. Susanto, M. Agung, H. Marubayashi
From the concepts of clean index of rings, nil clean index of rings, and weakly nil clean index of rings, we expand them by introducing the new concept, that is, trinil clean index of a ring. From any element a of a ring R with unity, we set τ(a): ={e ∈ R|e 3 = e and a - e ∈ Nil(R)}, where Nil(R) is the set of all nilpotent elements of R; trinil clean index of R is defined by sup{|τ(a)||a ∈ R} and it is denoted by Trinin(R). In this article, it will be investigated some properties of trinil clean index of any ring, ring homomorphism, and direct product. Some applications of determining trinil clean index of integral domains are also provided. We also determined the trinil clean index of n. © Published under licence by IOP Publishing Ltd.
Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Negeri Malang, Indonesia; Naruto University of Education, Japan
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