Finitely generated $\mathbb{C}$-subalgebras of $\mathbb{C}[x]$.
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
150337
Let $K$ be a subfield of $\mathbb{C}$ not contained in $\mathbb{R}$. Show that $K$ is dense in $\mathbb{C}$.
44685
Inner product on $C(\mathbb R)$
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
49521
In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
145104
$T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
132653
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
138410
Centralizer of $\mathbb{C}[G]$ in $\mathbb{C}[H]$
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
109688
Zero-dimensional ideals and finite-dimensional algebras
127044
Prove that a finitely-generated free module has a finite basis
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
158590
Why is it that if $[L:K]$ is finite, then $[L:K]$ is algebraic?