Show that $f (x) = ax + 1 \in R[x]$ is invertible in $R[x]$.
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
33030
Proof that $\inf A = -\sup(-A)$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
55902
Show $R[x]/(x)\cong R$
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
137920
Proving an equation with invertible matrices
94378
Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
61375
Meaning of $\mathbb{R}[x]$
158695
Prove that if $AB$ is invertible then $B$ is invertible.
12596
Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent iff $a_0,a_1,a_2,\ldots,a_n$ are nilpotent
6722
to show $f$ is a polynomial in $z$
157925
How to prove that the implicit function theorem implies the inverse function theorem?
84301
Showing that some Function on the Unit Disc is injective
26562
Inverse of $f(x)=\sin(x)+x$
119297
Finding invertible polynomials in polynomial ring $\mathbb{Z}_{n}[x]$