I'm looking for a reference in commutative algebra for the properties of the ring made of polynomials 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 which properties hold for it and for the modules over it.

Edit : As explained by YCor, it's the (semi)group algebra $k[\mathbf{R}^n_+]$ over the field $k$.

I would also like to add that my modules and ring are graded, exactly in the same way that $k[x, y]$ is a graded ring.

Thanks,