Finitely generated R-module is a field iff R is a field?
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
99423
Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
26368
Finitely generated graded modules over $K[x]$
14055
How to show that a finite commutative ring without zero divisors is a field?
28324
Inverse image of the sheaf associated to a module
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
46254
Why can't the Polynomial Ring be a Field?
73825
Every $R$-module is a quotient of a free module
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
80879
Can a quotient field ever be finitely generated as an algebra?
59687
Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
150206
Every finitely generated algebra over a field is a Jacobson ring
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module