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If $S$ is a finite subset of a commutative monoid, one can use the notation

$\prod_{x \in S} {x}$

for denoting the product of all elements of $S$.

It is rather obvious, that the same notation can also be used if $S$ is a finite commutative subset of a non-commutative monoid.

I am looking for a reference in the literature (algebra textbooks), where the latter case ($S$ is a finite commutative subset of a non-commutative monoid) was considered.

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    Why do you need a reference? Just restrict yourself to working in the commutative monoid generated by $S$.2012-07-16

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Theorem 18.7 in "Modern Algebra" by Seth Warner, p.151. (Dover Publications, New York, 1990).