Ida Fitriana Ambarsari, Santi Irawati, I. Made Sulandra, Hery Susanto, Angelina Chin Yan Mui, Hidetoshi Marubayashi, Muhamad Faikar Mustafidz Al Habibi
A ring R with unity is called clean if every element x R can be written as a sum of an idempotent and a unit element in ring R. Meanwhile, a ring with unity is called feebly clean, if every element r in the ring can be written as r = u + e - f, with ef = fe = 0, where u is a unit element in the ring and e, f is an idempotent element in the ring. [7] shows the existence of clean elements in a subring X3(D) of the matrix ring 3 × 3 over an integral domain D. Based on these results, we provide the set of all clean elements in the matrix ring X3(), we show the existence of feebly clean elements in the matrix ring X3(), and show the connections between those elements and feebly clean elements in the matrix ring X3(). These connections are different from [10]. © 2020 Author(s).
Department of Mathematics, Universitas Negeri Malang, Malang, Indonesia; Institute of Mathematical Science, University of Malaya, Malaysia; Department of Mathematics, Naruto University of Education, Naruto, Tokushima, Japan
