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Alternating**

Given an abelian group \((A,+)\) and a binary product \([\cdot,\cdot]:A\times A\to A\) (typically \((A,+)\) has the additional structure of being a vector space and \([\cdot,\cdot]\) is also bilinear, but this is not required), one says that \([\cdot,\cdot]\) is alternating if \(\forall x\in A:[x,x]=0\).