Derivations with invertible values in rings with involution
type: Item
instance of: scholarly article
title: Derivations with invertible values in rings with involution
zbMATH Open document ID: 0587.16022
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The authors extend the result of \textit{J. Bergen, I. N. Herstein} and \textit{C. Lanski} [Can. J. Math. 35, 300-310 (1983; Zbl 0522.16031)] which characterizes rings having a derivation whose nonzero values are invertible, to the case of involutions. Specifically let R be a 2-torsion free semi-prime ring with involution and derivation d satisfying d(s) is zero or invertible for each symmetric element s. The authors prove that R must be either a division ring D, \(M_ 2(D)\), the direct sum of either of these with its opposite ring, or \(M_ 4(F)\) with symplectic involution. The proof is computational and makes clever use of the Jacobson density theorem.
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16D70
zbMATH DE Number: 3941744
zbMATH Keywords: derivation
zbMATH Keywords: semi-prime ring with involution
zbMATH Keywords: symmetric element
zbMATH Keywords: division ring
zbMATH Keywords: direct sum
zbMATH Keywords: symplectic involution
zbMATH Keywords: Jacobson density theorem
author: Antonio Giambruno
author: Paola Misso
author: C. Polcino Milies
MaRDI profile type: Publication
full work available at URL: pjm.1986.123.47
OpenAlex ID: W2078744858
DOI: 10.2140/PJM.1986.123.47
description: scientific article; zbMATH DE number 3941744