For several classes of noncommutative algebras, every element splits as a central element plus a sum of commutators, and a rigidity theorem holds for twisted group algebras of locally finite groups.
Ancochea, On semi-automorphisms of division algebras,Ann
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A note on additive commutator groups in certain algebras
For several classes of noncommutative algebras, every element splits as a central element plus a sum of commutators, and a rigidity theorem holds for twisted group algebras of locally finite groups.