Let $f$ is a $n$-ary function (where $n$ is any index set) and let every argument of $f$ may be zero or non-zero (for example, we can consider arguments of $n$ being posets with least element which I call "zero").
Are there any special name for such $f$ that every argument can be restored knowing the value of the function, provided that every of the $n$ arguments is non-zero?
An example of such $f$ is cartesian product of $n$ sets (where zero is the empty set).