A Remark on n-absorbing Ideals of Principal Ideal Domains

Let R be a commutative ring with identity 1 ≠ 0. General-izing the notion of prime ideals in R, Anderson and Badawi introduced the notion of n-absorbing ideals in R. We introduce the notion of n- absorbing domains which is a generalization of an integral domain. We investigate all n-absorbing ideals in a PID R and hence prove that Z_m is an n-absorbing domain if and only if m = p₁^r1 p₂^r2 p₃^r3 …p_k^rk where k ≤ n and r1 + r2 + r3 + … + rk ≤ n.