Vella Nafisatul Ilmiah, Santi Irawati, Hidetoshi Marubayashi
A unital ring R is called almost clean if every element of R can be written as the sum of a regular and an idempotent element in R. This article aims to construct a general form of almost clean ideal of matrix ring T2(p3), p prime, which is a follow up of clean ideal and nil clean ideal. The procedure is finding all regular and idempotent elements in T2(p3), p prime and then constructing all general forms of its almost clean elements. The result shows that from these almost clean elements, there exists the almost clean ideal by adding some conditions. © 2024 Author(s).
Mathematics Department, Universitas Negeri Malang, Malang, Indonesia; Department of Mathematics, Naruto University of Education, Naruto, Japan
