Bulletin of the
Korean Mathematical Society BKMS

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 a 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.

Keywords: Mid ring, mp-ring, p.f.~ring, von Neumann regular ring, zero-dimensional ring, N-pure ideal, pure ideal

MSC numbers: 13A15, 13C05, 13C10, 13C15, 16E50