On some special generalized functional identities.
type: Item
instance of: scholarly article
title: On some special generalized functional identities.
zbMATH Open document ID: 1062.16032
author: Daniel Eremita
published in: Taiwanese Journal of Mathematics
publication date: 2004-11-01T00:00:00Z
review text: A theorem by \textit{M. A. Chebotar} [J. Algebra 202, No. 2, 655-670 (1998; Zbl 0907.16008)] shows that the existence of a non-standard solution of a generalized functional identity (GFI) on a prime ring \(R\) implies that \(R\) is a GPI ring. The paper under review studies some special GFI's on \(R\) for which a more refined conclusion can be derived. More precisely, the following types of GFI's are considered: (i) GFI's that have only standard solutions in any case, i.e. regardless of whether \(R\) is GPI or not, (ii) GFI's for which the existence of a non-standard solution yields that their coefficients lie in the socle of the central closure, and (iii) GFI's for which the existence of a non-standard solution yields some information about the structure of the associated division algebra of the central closure of \(R\).
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 2113502
zbMATH Keywords: generalized functional identities
zbMATH Keywords: prime rings
zbMATH Keywords: generalized polynomial identities
zbMATH Keywords: extended centroids
reviewed by: Matej Brešar
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407621
OpenAlex ID: W4233257151
DOI: 10.11650/TWJM/1500407621
description: scientific article; zbMATH DE number 2113502