When did we move from $\mathbb{Z}\left[\sqrt{d}\right]$ to the ring of integers $\mathcal{O}_{\mathbb{Q}\left[\sqrt{d}\right]}$ and why?
104643
Why do we use this definition of "algebraic integer"?
64179
What is the difference between the standard representants of $\mathbb Z/q\mathbb Z$?
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
126429
Let $R=\mathbb{Z}\left[\sqrt{−5}\right]$. Let $I=\left(2,1+\sqrt{−5}\right)$. Show $I^2 = (2)$ in $R$.
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
77903
Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
95863
Describe the units in $\mathbb{Z}[\sqrt{-d}]$
31216
Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?
130159
Meaning of ring notation $\Bbb Z_{(p)}$ in commutative algebra [localization]
20097
Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
47041
What are the conditions for integers $D_1$ and $D_2$ so that $\mathbb{Q}[\sqrt {D_1}] \simeq \mathbb{Q}[\sqrt {D_2}]$ as fields.
34599
Number of ring homomorphisms from $\mathbb Z_{12}$ to $\mathbb Z_{28}$.
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?