Let be finitely generated as a -algebra.
Then can I say is finitely generated as a -module?
I cannot understand some part of definitions about finitely generated...
The polynomial algebra is finitely generated as an algebra, but it is NOT
a finitely generated module...
** f.g. algebra = all the elements are finite sums of finite products of some elements in the algebra
** f.g. module = all the elements are finite sums AND PRODUCTS BY SCALARS of some elements in the module.