Existence, automatic continuity and invariant submodules of generalized derivations on modules
type: Item
instance of: scholarly article
title: Existence, automatic continuity and invariant submodules of generalized derivations on modules
zbMATH Open document ID: 1257.47040
author: G. H. Esslamzadeh
author: Hoger Ghahramani
published in: Aequationes Mathematicae
publication date: 2012-11-21T00:00:00Z
review text: The authors first show that free modules and projective modules always have nontrivial generalized derivations. Then they prove that every minimal prime submodule of a left \(\mathcal A\)-module \(\mathcal{M}\), where \(\mathcal A\) is a \(\mathbb C\)-algebra, is invariant under every generalized derivation. Furthermore, the authors obtain analogs of Posner's theorem for generalized derivations. In the case when \(\mathcal{A}\) is a Banach algebra and \(\mathcal{M}\) is a Banach left \(\mathcal{A}\)-module, the authors study the existence of continuous generalized derivations and automatic continuity of generalized derivations.
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 46H40
zbMATH DE Number: 6109265
zbMATH Keywords: generalized derivation
zbMATH Keywords: \(\mathbb C\)-algebra
zbMATH Keywords: left module
reviewed by: Ajda Fošner
MaRDI profile type: Publication
full work available at URL: s00010-012-0127-0
OpenAlex ID: W1976945556
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DOI: 10.1007/S00010-012-0127-0
description: scientific article; zbMATH DE number 6109265