Gupta, Vishnu Two elementary commutativity theorems for generalized Boolean rings. (English) Zbl 0880.16015 Int. J. Math. Math. Sci. 20, No. 2, 409-411 (1997). Let \(R\) be an associative ring with unity satisfying the identity \([x^m-x^n,y]=0\). The author proves the commutativity of \(R\) if \(R\) satisfies one of the following conditions: (i) \(m\), \(n\) are relatively prime integers, one of which is even; (ii) \(R\) is a 2-torsion free ring and \(m=2^k(q+1)\), \(n=2^k\cdot q\). Reviewer: Yu.N.Mal’tsev (Barnaul) MSC: 16U70 Center, normalizer (invariant elements) (associative rings and algebras) 16R50 Other kinds of identities (generalized polynomial, rational, involution) 16U80 Generalizations of commutativity (associative rings and algebras) 06E20 Ring-theoretic properties of Boolean algebras Keywords:commutativity theorems; generalized Boolean rings; polynomial identities PDFBibTeX XMLCite \textit{V. Gupta}, Int. J. Math. Math. Sci. 20, No. 2, 409--411 (1997; Zbl 0880.16015) Full Text: DOI EuDML