Free commutative monoid
= Free commutative monoid
{title2=$\mathbb N^d$}
The <free commutative monoid> on $d$ generators consists of the nonnegative integral sums of those generators, with unique coefficients. Its <semigroup algebra> over a <commutative ring> is the <polynomial ring> in $d$ variables. In a smooth toric chart, the dual-cone lattice points form such a monoid, yielding affine-space coordinates.