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### Free algebra over infinite alphabet

Is it possible to work with a free algebra over an infinite alphabet ? Or to define an Infinite ring of non-commutative polynomials ? I need one of these structures to work with the quasi shuffle product.

 2 retagged FrédéricC 4131 ●3 ●37 ●85

### Free algebra over infinite alphabet

Is it possible to work with a free algebra over an infinite alphabet ? Or to define an Infinite ring of non-commutative polynomials ? I need one of these structures to work with the quasi shuffle product.