On commutativity of P.I. rings
type: Item
instance of: scholarly article
title: On commutativity of P.I. rings
zbMATH Open document ID: 0537.16028
DOI: 10.1007/BF02189668
author: Howard E. Bell
published in: Aequationes Mathematicae
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/136986
review text: The author proves the commutativity of some classes of rings satisfying a polynomial identity \([X,Y]=f(X,Y)\), which does not hold for total matrix algebras over a field. Here f(X,Y) belongs to the commutator ideal of the free associative algebra over a commutative ring F. In particular, if \(\phi(X),\psi(X)\in X^ 2F[X],\) then the identity \([X,Y]=[\phi(X),Y]+[\psi(Y),X]\) yields commutativity.
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16Rxx
zbMATH DE Number: 3853313
zbMATH Keywords: commutativity
zbMATH Keywords: polynomial identity
zbMATH Keywords: commutator ideal
MaRDI profile type: Publication
cites work: Prime Rings Having Polynomial Identities with Arbitrary Coefficients
cites work: Duo Rings: Some Applications to Commutativity Theorems
cites work: On some commutativity theorems of Herstein
cites work: The Structure of a Certain Class of Rings
cites work: Über einen Satz von Herstein und Nakayama
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description: scientific article; zbMATH DE number 3853313