Consider set $\mathbb{Z}[\sqrt{-5}] = \{a+b\sqrt{5}i : a,b \in \mathbb{Z} \}$ show that it is a ring
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
66451
In a ring, how do we prove that a * 0 = 0?
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
72507
Does $ab=1$ imply $ba=1$ in a ring?
12110
How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
155745
Ideals of $\mathbb{Z}[X]$
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
52966
Rings, ideals and units-proof
44528
The only natural number $x$ for which $x+\sqrt{-2}$ is a cube in $\mathbb{Z}[\sqrt{-2}]$ is $x=5$
148550
Units in quotient ring of $\mathbb Z[X]$
17239
Find all ideals of ${\mathbb{Z}_n}$
126429
Let $R=\mathbb{Z}\left[\sqrt{−5}\right]$. Let $I=\left(2,1+\sqrt{−5}\right)$. Show $I^2 = (2)$ in $R$.
35279
It's $\mathbb{Z}\subseteq \mathbb{Z}[X]/(X^5-1)$ an integral extension?
50908
Showing a Ring and an Ideal are equal