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Propreties of a subring of a 'completed' of k(X_1, X_2, ..., X_n)

I'm looking for a reference in commutative algebra for the propreties of the ring made of polynoms in n indeterminate over a field k with "real exponents".

I don't even know the name of this ring, and I would like to know wich propreties hold for it and for the modules over it.

Thanks,