From any element a of a ring R with unity, we set τ(a) = {e ∈ R|e3 = e and a - e 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). Motivated by the trinil clean index of any ring Zn for any positive integer n ≥ 2, we expand these results by determined the trinil clean index of upper triangular matrix 2 × 2 over Zn which n is positive integer greater than 2.
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