On radicals of ring extensions
type: Item
instance of: scholarly article
title: On radicals of ring extensions
zbMATH Open document ID: 0607.16005
DOI: 10.1007/BF01197136
author: Shalom Feigelstock
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: \textit{B. de la Rosa} and \textit{G. A. P. Heyman} have shown that a ring radical R satisfies \(R(A)=R(A^*)\), for every Dorroh extension \(A^*\) of a ring A, if and only if \(R({\mathbb{Z}})=0\), \({\mathbb{Z}}\) the ring of integers [Arch. Math. 42, 516 (1984; Zbl 0522.16008)]. The author of this paper proves the following fact. Theorem. Let R be a ring radical, and let B be a ring. The following are equivalent: 1) There exists an extension \(R(B)^*\) of R(B) by B such that \(R[R(B)^*]=R(B)\). 2) \(R(B)=0\). 3) For every extension \(A^*\) of a ring A by B, \(R(A)=R(A^*)\).
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 16S20
zbMATH DE Number: 3981368
zbMATH Keywords: radical
zbMATH Keywords: Dorroh extension
reviewed by: I. Kh. Bekker
MaRDI profile type: Publication
cites work: A note on radicals and the Dorroh extension
full work available at URL: https://doi.org/10.1007/bf01197136
OpenAlex ID: W2077428936
description: scientific article; zbMATH DE number 3981368