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.