Matrix rings over a principal ideal domain in which elements are nil-clean

An element of a ring r is called nil-clean if it is the sum of an idempotent and a nilpotent element. a ring is called nil-clean if each of its elements is nil-clean. s. breaz et al. in [1] proved their main result that the matrix ring m_n(f) over a field f is nil-clean if and only if f≈f2, where f_2 is the field of two elements. m. t. kosan et al. generalized this result to a division ring. in this paper, we show that the n*n matrix ring over a principal ideal domain r is a nil-clean ring if and only if r is isomorphic to f_2. also, we show that the same result is true for the 2*2 matrix ring over an integral domain r. as a consequence, we show that for a commutative ring r, if m_2(r) is a nil-clean ring, then dimr = 0 and charr/j(r) = 2.