Use this tag for questions related to the subset of quadratic integers contained in a quadratic field.

35 questions
Filter by
Sorted by
Tagged with
23 views

30 views

### Quadratic Integer Ring $\mathbb{Z}[\sqrt{-14}]$, show that $7+\sqrt{-14} \notin (7)$

I just want to make sure I am getting this correct, as I am just learning ring theory and quadratic integer rings. Let $\alpha = 7 + \sqrt{-14}$. To show that $\alpha \notin (7)$ I will show a ...
43 views

### Prime and Maximal Ideals of $\mathbb{Z}[\sqrt{-10}]$

I want to solve the following questions: For $R = \mathbb{Z}[\sqrt{-10}]$ and $I = (\sqrt{-10})$ I ) Is $I$ a prime ideal? II) Is $I$ a maximal ideal? This is equivalent to asking if $\frac{R}{I}$ ...
174 views

12 views

### Some reference on quadratic rings or introductory algebraic number theory. [duplicate]

I have found many posts on this matter. But none of them fulfills my purpose. So I am describing my situation briely. I have read ring theory from Dummit & Foote. I have been reading some field ...
160 views

100 views

### Existence of integers $a$ and $b$ such that $p = a^2 +ab+b^2$ for $p = 3$ or $p\equiv 1 \mod 3$

**Eisenstein primes, existence of integers ** I am working in subring $$R = \{a + b\zeta : a,b \in \mathbb{Z}\}$$ of $\mathbb{C}$ where $\zeta = \frac{1 + \sqrt{-3}}{2} \in \mathbb{C}$. I want to ...
104 views