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.