Radical formula and prime submodules
type: Item
instance of: scholarly article
title: Radical formula and prime submodules
zbMATH Open document ID: 1117.13005
author: Abdulrasool Azizi
published in: Journal of Algebra
publication date: 2007-01-26T00:00:00Z
review text: The envelope \(E(B)\) of a submodule \(B\subset M\) of a module \(M\) over a commutative ring \(R\) is a module version of the radical of an ideal. This paper introduces the \(n\)th envelope \(E_n(B) = E(\langle E_{n-1}(B)\rangle), E_0(B)=B\). It is shown that if \(R\) is an arithmetical ring of finite Krull dimension \(n\), then \(\langle E_n(B)\rangle = \text{rad}(B)\).
reviewed by: Reinhard Laubenbacher
Mathematics Subject Classification ID: 13A10
zbMATH DE Number: 5118829
zbMATH Keywords: arithmetical rings
zbMATH Keywords: prime submodules
zbMATH Keywords: radical formula
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.07.006
OpenAlex ID: W2007162255
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DOI: 10.1016/J.JALGEBRA.2006.07.006
description: scientific article; zbMATH DE number 5118829