Tensor square of a Lie ring

Definition
Suppose $$L$$ is a Lie ring. The tensor square of $$L$$, denoted $$L \otimes L$$ or $$\bigotimes^2 L$$, is defined as the tensor product of $$L$$ with itself, where both parts of the compatible pair of actions are taken as the adjoint action on itself.

Related notions

 * Exterior square of a Lie ring: This is the quotient of the tensor square by all the tensors of the form $$x \otimes x, x \in L$$.
 * Tensor square of a group
 * Exterior square of a group