# Determining whether module is free for polynomial/power series rings

Say I have two modules

```
R = QQ[[x, y, z]]
S = QQ[[x, y^2, z]]
```

(we can also make `R`

and `S`

as polynomial rings).

`R`

is naturally an `S`

module as `S`

can act on `R`

by multiplication.

Is there a command which determines whether `R`

is free over `S`

and the rank?

Shouldn't the firs line be

I can't make head or tail of

What is this supposed to mean ?

Hello, I just made that as an example. So to make thing simpler, let's ignore the +1. If we think of polynomial ring first,

is the polynomial ring with variables (generators if you like) x,y,z. So terms here look like

where a is a rational number. So

will be polynomial ring with variables x,y^2, z. Terms here look like

So

will be power series ring in variables x, y^2, z.