Let $\varphi$ be an $n$-linear functional on a vector space $X$. Suppose that $\varphi$ has the property that, for all $(x_1,\ldots,x_n) \in X^n$, we have $$ \varphi(x_1,\ldots,x_n) + \varphi(x_2,\ldots,x_n,x_1) + \varphi(x_3,\ldots,x_n,x_1,x_2) + \ldots + \varphi(x_n,x_1,\ldots,x_{n-1}) = 0.$$ Is anyone aware of any special terminology for such a functional? In the case $n=2$, this says that $\varphi$ is alternating.
Sorry for the somewhat unmotivated question. I do have some particular functionals in mind, but I don't think the context is all that relevant.