Centralizing maps in prime rings with involution
Date
2010-04-28T21:15:43Z
Authors
Bresar, M.
Martindale, W. S.
Miers, C. Robert
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Abstract
Let R be a prime ring with involution, of characteristic \ne 2, with center Z, skew elements K, and extended centroid C. Theorem. Suppose [K,K] \ne {0} and f:K->K is an additive map such that [f(x),x] \in Z for all x \in K. Then, unless R is an order in a 16-dimensional central simple algebra, there exists \lambda \in C and an additive map \mu: K -> C such that f(x)=\lambda x + \mu(x) for all x \in K.
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technical reports (mathematics and statistics)