Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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N-PURE IDEALS AND MID RINGS

  • Aghajani, Mohsen (Department of Mathematics Faculty of Basic Sciences University of Maragheh)
  • Received : 2021.09.19
  • Accepted : 2021.12.06
  • Published : 2022.09.30
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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 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.

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Acknowledgement

The author would like to thank the referee for careful reading of the present paper.

References

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