Prove that if $I$ is maximal, then $R[X]$ is a PID.
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
113391
Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too.
154837
mapping properties of $(1−z)^i$
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
121845
Quotient of polynomials, PID but not Euclidean domain?
92588
Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
143313
Maximal solution differential equation
30356
$a =\prod_{i = 1}^{r} p_{i}^{ai}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...
111122
Proof of a theorem in Hilbert's system
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
149783
$\mathbb Z\times\mathbb Z$ is principal but is not a PID
111191
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
68275
Primitive Root Theorem Proof
91557
Show that total orders are maximal orders
78455
Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.
154076
How to show this property of $\mathbb{RP}^{n}$.