Prime one-sided ideals of a finite normalizing extension
type: Item
instance of: scholarly article
title: Prime one-sided ideals of a finite normalizing extension
zbMATH Open document ID: 0607.16022
author: Taichi Nakamoto
published in: Osaka Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A right ideal I of a ring R is called prime if, for any two right ideals X and Y of R, XY\(\subseteq I\) implies that \(X\subseteq I\) or \(Y\subseteq I\). In this note, some well-known facts about prime two-sided ideals in finite normalizing (centralizing, intermediate) ring extensions, such as ''Lying Over'', ''Cutting Down'', etc., are extended to the case of prime right ideals, usually under additional assumptions on the ring extension in question.
Mathematics Subject Classification ID: 16S20
Mathematics Subject Classification ID: 16Dxx
zbMATH DE Number: 3981385
zbMATH Keywords: finite normalizing (centralizing, intermediate) ring extensions
zbMATH Keywords: Lying Over
zbMATH Keywords: Cutting Down
zbMATH Keywords: prime right ideals
reviewed by: Martin Lorenz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3981385