Definition:Monomial of Free Commutative Monoid/Multiplication

Definition
The set of mononomials over $\left\{{X_j: j \in J}\right\}$ has multiplication $\circ$ defined by:


 * $\displaystyle \left({\prod_{j \mathop \in J} X_j^{k_j}}\right) \circ \left({\prod_{j \mathop \in J} X_j^{k_j'}}\right) = \left({\prod_{j \mathop \in J} X_j^{k_j + k_j'}}\right)$

which using multiindex addition notation reads:


 * $\mathbf X^k \circ \mathbf X^{k'} = \mathbf X^{k + k'}$