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Bi-additive Maps and Commutativity in Rings

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Abstract

We study bi-additive maps with trace which is skew-commuting or skew-centralizing on rings with left identity; and we investigate commutativity in prime and semiprime rings admitting nonzero derivations d and δ such that [d(x),δ(y)] = 0 for all x, y in some nonzero one-sided ideal.

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