Can you give me some examples of infinitely generated modules over commutative rings, other than $A[x_1,\ldots,x_n,\ldots]$?
Thanks a lot!
Can you give me some examples of infinitely generated modules over commutative rings, other than $A[x_1,\ldots,x_n,\ldots]$?
Thanks a lot!
One variable is enough! $A[X]$ over $A$ is infinitely generated as an $A$-module.
Other suggestions in the comments: $\mathbb{Q}$ over $\mathbb{Z}$ or an infinite direct sum of copies of $\mathbb{Z}$ over $\mathbb{Z}$.