Röhmel's equation for quadratic forms
type: Item
instance of: scholarly article
title: Röhmel's equation for quadratic forms
zbMATH Open document ID: 0632.10020
DOI: 10.1007/BF01840125
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137224
review text: Let \(q: x\to A\) satisfy \(q(0)=0\) and \(q(ax+y)+q(x-ay)=(1+a)[q(x)+q(y)]\) for all x,y\(\in X\) and \(a\in A\), where A is a commutative ring with 1 and X is an A-module. The author proves that q is a quasi-quadratic form if the only \(k\in A\), which satisfies \(2k=0\) and \((a^ 4-a^ 2)k=0\) for all a in A, is \(k=0\). It is also proved that a quasi-quadratic form becomes a quadratic form if and only if the only function \(D: A\to A\) satisfying \(D(a+b)=D(a)+D(b),\) \(D(1)=0\) and \(D(a^ 2b)=a^ 2 D(b)\) is \(D=0\).
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 4027568
zbMATH Keywords: commutative ring
zbMATH Keywords: quasi-quadratic form
author: T. M. K. Davison
reviewed by: Sunder Lal
MaRDI profile type: Publication
cites work: Jordan derivations and quasi-bilinear forms
cites work: The Definition of a Quadratic Form
cites work: Q5345222
cites work: Eine Charakterisierung quadratischer Formen durch eine Funktionalgleichung
OpenAlex ID: W2014219623
description: scientific article; zbMATH DE number 4027568