N-pure ideals and mid rings
Commutative Algebra
2021-01-28 v2
Abstract
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.
Cite
@article{arxiv.2011.02134,
title = {N-pure ideals and mid rings},
author = {Mohsen Aghajani},
journal= {arXiv preprint arXiv:2011.02134},
year = {2021}
}