If $R \subseteq k[X]$, then $R$ is a finitely generated $k$-algebra.
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
17378
Characterize finite dimensional algebras without nilpotent elements
121465
$R[x]$ has a subring isomorphic to $R$.
9806
$M$ finitely generated if submodule and quotient are finitely generated.
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
101669
Cardinality of the Set of all finite subset of $\mathbb{R}$
150206
Every finitely generated algebra over a field is a Jacobson ring
65098
Number of $\sigma$  -Algebra on the finite set
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
93111
Finiteness of the Algebraic Closure
153622
Are intermediate rings of finitely generated ring extensions also finitely generated?
109080
Is the kernel of a map to a finitely presented module finitely generated?
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
16643
A slick proof that a field which is finitely generated as a ring is finite
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?