Definition:Free Commutative Monoid
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Definition
The free commutative monoid on an indexed set $X = \family {X_j: j \in J}$ is the set $M$ of all monomials under the standard multiplication.
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That is, it is the set $M$ of all finite sequences of $X$.
Also known as
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Some sources refer to this as the free monoid on $X$, dropping the commutativity part.
Also see
Sources
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.1$: Monoids