Let $R$ be a ring such that $\Bbb Z \subset R \subset \Bbb Q$. Show that $R$ is a PID.
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
107821
The ring of integers of $\mathbf{Q}[i]$
1315
Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
154076
How to show this property of $\mathbb{RP}^{n}$.
127418
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
52966
Rings, ideals and units-proof
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
102282
Let $R$ be a PID, and let $\pi\in R$ be prime. Is it $R/\langle\pi\rangle \times R/\langle \pi\rangle$ a cyclic $R$-module?
21604
A complete ring with respect to an ideal
11573
Rings and some of their properties