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Rings with ideal centres. (English) Zbl 1354.16038

This paper provides nontrivial examples of rings \(R\) in which the center is an ideal, and it gives elementary proofs of three known commutativity theorems under the additional hypothesis that the center of \(R\) is an ideal.

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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