Bull. Korean Math. Soc. 2022; 59(5): 1237-1246
Online first article September 13, 2022 Printed September 30, 2022
https://doi.org/10.4134/BKMS.b210694
Copyright © The Korean Mathematical Society.
Mohsen Aghajani
University of Maragheh
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
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