Isn't a subalgebra of a finitely generated k-algebra always finitely generated?
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
34065
Submodule of free module over a p.i.d. is free even when the module is not finitely generated?
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
18066
Prove that any non-zero-divisor of a finite dimensional algebra has an inverse
105333
Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
145507
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
2719
Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
109688
Zero-dimensional ideals and finite-dimensional algebras
95930
Finitely generated modules over a Noetherian ring are Noetherian
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
92309
The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
16643
A slick proof that a field which is finitely generated as a ring is finite
105818
Given an associative $F$-algebra do there necessarily exist elements $a_1,a_2 \in K$ satisfying $a_1*a_2=a$?
109080
Is the kernel of a map to a finitely presented module finitely generated?
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal