A commutativity theorem for rings. II
type: Item
instance of: scholarly article
title: A commutativity theorem for rings. II
zbMATH Open document ID: 0575.16017
author: H. Komatsu
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: [Part I, cf. Math. J. Okayama Univ. 26, 109-111 (1984; Zbl 0568.16017).] The author generalizes a theorem for commutativity of a ring given by \textit{T. P. Kezlan} [Math. Jap. 29, 135-139 (1984; Zbl 0538.16028)]. This generalization is the following theorem: ''Let \(n>0\), r,s, and t be nonnegative integers and let \(f(X,Y)=\sum^{r}_{i=1}\sum^{s}_{j=2}f_{ij}(X,Y)\) be a polynomial in two noncommuting indeterminates X, Y with integer coefficients such that each \(f_{ij}\) is a homogeneous polynomial with degree i in X and degree j in Y and the sum of the coefficients of \(f_{ij}\) equals zero. Suppose a left s-unital ring R satisfies the polynomial identity \(X^ t[X^ n,Y]-f(X,Y)=0\). If either \(n=1\) or \(r=1\) and R has the property Q(n), then R is commutative.''
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16Rxx
zbMATH DE Number: 3918596
zbMATH Keywords: commutativity
zbMATH Keywords: left s-unital ring
zbMATH Keywords: polynomial identity
reviewed by: Mirela Ştefănescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3918596