Krull’siPrincipal Ideal Theorem for Locally Noetherian Rings

Volume 25 , Issue 1 , June 2023 , Pages 206-213

Authors

Baban Othman Majeed 1 ; Adil Kadir Jabbar 1 ; Chwas Abas Ahmed 1

1 Department of Mathematics-College of Science-University of Sulaimani, Sulaymaniyah-Iraq

DOI logo 10.17656/spa.10890

Keywords

Abstract

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.

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  • Published at20 June 2023

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