×

On commutativity of one-sided \(s\)-unital rings. (English) Zbl 0776.16016

Let \(R\) be a left \(s\)-unital ring, and let \(r=r(y)>1\), \(s\) and \(t\) be non negative integers. Suppose that \(R\) satisfies the polynomial identity \([xy-x^ s y^ r x^ t,x]=0\) for all \(x,y\in R\). Then \(R\) is commutative.

MSC:

16U70 Center, normalizer (invariant elements) (associative rings and algebras)
16U80 Generalizations of commutativity (associative rings and algebras)
16N60 Prime and semiprime associative rings
16R40 Identities other than those of matrices over commutative rings
PDFBibTeX XMLCite
Full Text: DOI EuDML