Rings whose additive endomorphisms are \(n\)-multiplicative. II
type: Item
instance of: scholarly article
title: Rings whose additive endomorphisms are \(n\)-multiplicative. II
zbMATH Open document ID: 0762.16015
DOI: 10.1007/BF02454380
published in: Periodica Mathematica Hungarica
publication date: 1993-02-08T00:00:00Z
review text: [For part I cf. Bull. Aust. Math. Soc. 39, No. 1, 11-14 (1989; Zbl 0651.16016).] A ring \(R\) is called an \(AE_ n\)-ring, \(n\geq 2\) a positive integer, if every endomorphism \(\varphi\) of the additive group of \(R\) satisfies \(\varphi(a_ 1a_ 2\dots a_ n)=\varphi(a_ 1)\varphi(a_ 2)\dots \varphi(a_ n)\) for all \(a_ 1,\dots,a_ n\in R\). Several results concerning the structure of \(AE_ n\)-rings are obtained in this note, including an (incomplete) description of \(AE_ n\)-rings \(R\) satisfying \(R_ tR^{n-1}\neq 0\), where \(R_ t\) is the torsion ideal in \(R\).
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 20K30
zbMATH DE Number: 118335
zbMATH Keywords: endomorphism
zbMATH Keywords: additive group
zbMATH Keywords: \(AE_ n\)-rings
zbMATH Keywords: torsion ideal
author: Shalom Feigelstock
MaRDI profile type: Publication
cites work: Rings whose additive endomorphisms are ring endomorphisms
cites work: Q3791298
cites work: Rings whose additive endomorphisms are multiplicative
cites work: Q4040250
cites work: Rings whose additive endomorphisms are N-multiplicative
cites work: On rings whose additive endomorphisms are multiplicative
description: scientific article; zbMATH DE number 118335