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Commutativity of right \(s\)-unital rings with polynomial constraints. (English) Zbl 0935.16023

The principal theorem of the paper asserts that a right \(s\)-unital ring must be commutative if it satisfies an identity of the form \([(x^my^rx^s)^n-yx^t,x]=0\), where \(m\), \(n\), \(r\), \(s\) and \(t\) are nonnegative integers and at least one of \(r\) and \(n\) is different from \(1\). Unfortunately, the proof has an error right at the beginning. There are two other commutativity theorems for right \(s\)-unital rings satisfying constraints involving commutators.

MSC:

16U70 Center, normalizer (invariant elements) (associative rings and algebras)
16U80 Generalizations of commutativity (associative rings and algebras)
16R50 Other kinds of identities (generalized polynomial, rational, involution)
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