Commutativity of generalized Boolean rings. (English) Zbl 0657.16020

Quadri, Murtaza A.; Ashraf, Mohd.

Publ. Math. Debr. 35, No. 1-2, 73-75 (1988).

The following results are proved: (i) If \(n>1\) is a fixed integer and R is a semi-prime ring in which \((xy)^ n-xy\) is central for every x,y in R, then R is commutative. (ii) If n is a fixed positive integer and R is a ring with unit 1 in which \(x^{n+1}-x^ n\) is central for all \(x\in R\), then R is commutative.

Reviewer: M.Abad

MSC:

16U70	Center, normalizer (invariant elements) (associative rings and algebras)
16U99	Conditions on elements
06E20	Ring-theoretic properties of Boolean algebras

Keywords:

semi-prime ring; central; commutative