Is a multilinear polynomial of variables $x_1, \dots, x_n$ over a ring defined as a monomial $c \prod_{i=1}^n x_i$, where $c$ is a constant from the ring?
Equivalently, is a multilinear polynomial function of variables $x_1, \dots, x_n$ over a ring same as a multilinear mapping of $x_1, \dots, x_n$?
My confusion comes from Wikipedia
In algebra, a multilinear polynomial is a polynomial that is linear in each of its variables. In other words, no variable occurs to a power of 2 or higher; or alternatively, each monomial is a constant times a product of distinct variables. ... The degree of a multilinear polynomial is the maximum number of distinct variables occurring in any monomial.
It seems to suggest a multilinear polynomial can have more than one monomial terms. Thanks!