Krull’s Principal Ideal Theorem for Locally Noetherian Rings

Authors

  • Baban Othman Majeed Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Adil Kadir Jabbar Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Chwas Abas Ahmed Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.17656/jzs.10909

Keywords:

Locally Noetherian Rings, Heights of Prime Ideals, Minimal Prime Ideals, Krull’s Principal Ideal Theorem

Abstract

A ring is Locally Noetherian if is Noetherian for each prime ideals of. In this paper we study Locally Noetherian rings. We show that Krull’s Principal Ideal Theorem and Generalized Principal Ideal Theorem are also true for Locally Noetherian rings. In general, Locally Noetherian rings do not have finitely many minimal prime ideals, a sufficient condition is given under which they have finitely many minimal prime ideals.

References

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Published

2023-06-20

How to Cite

Krull’s Principal Ideal Theorem for Locally Noetherian Rings. (2023). Journal of Zankoy Sulaimani - Part A, 25(1), 9. https://doi.org/10.17656/jzs.10909

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