Krull’siPrincipal Ideal Theorem for Locally Noetherian Rings - Majeed, Baban Othman; Jabbar, Adil Kadir; Ahmed, Chwas Abas (Sulaimani Journal for Pure and Applied Sciences, 2023)
A ring 𝑅 is Locally Noetherian if 𝑅𝒫 is Noetherian for each prime ideals 𝒫 of 𝑅. 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.
Keywords: Locally Noetherian Rings Heights of Prime Ideals Minimal Prime Ideals Krulls Principal Ideal Theorem