Comparing proof of $R[[x]]^*$ consists of $\sum_{n \geq 0}a_{n}x^n (a_{n} \in R) ,a_{0} \in R^* ,R$ an integral domain to $R$ a ring.
4353
Unit group of power series ring
86054
$r+r^{-1}$ integral implies $r^n+r^{-n}$ integral
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
62951
Is there a more direct way of proving that this ring is an integral domain?
57031
Ring of fractions of $R$ is integral over $R$
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
4196
A valid proof for the invariance of domain theorem?
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
67706
If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
124562
$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$
87078
Prove the following set is an ideal of the ring $Z[x]$
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
158311
What is the dimension of $R[[X]]$ where $R$ is a Noetherian ring?