  In this paper, we introduce the concept of N-pure ideal as a generalization
of pure ideal. Using this concept, a new and interesting type of rings is
presented, we call it mid ring. Also, we provide new characterizations for von
Neumann regular and zero-dimensional rings. Moreover, some results about
mp-ring are given. Finally, a characterization for mid rings is provided. Then
it is shown that the class of mid rings is strictly between the class of
reduced mp-rings (p.f. rings) and the class of mp-rings.
