Quadratic Integer Rings.

Conrad, B. Quadratic Integer Rings.

Type

Web resource

Intellectual base

Web

Link

https://math.stanford.edu/~conrad/210BPage/handouts/quadint.pdf

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Quadratic Field
  • The integral layer. The ring of integers is \(\mathcal O_K= \begin{cases} \mathbb Z[(1+\sqrt d)/2],&d\equiv1\pmod4,\\ \mathbb Z[\sqrt d],&d\equiv2,3\pmod4, \end{cases}\) and the field discriminant is respectively $D_K=d$ or $D_K=4d$.
• Quadratic Integer
  • Under the field-inclusive convention, “quadratic integers of \(K\)” means every element of the ring of integers \(\mathcal O_K\) of a fixed quadratic field \(K\), including the rational integers \(\mathbb Z\), whose individual degree over \(\mathbb Q\) is one.

    This sourceComputes the integral closure \(\mathcal O_K\) of \(\mathbb Z\) in \(K=\mathbb Q(\sqrt d)\) from trace and norm and proves the discriminant-dependent integral basis. <https://math.stanford.edu/~conrad/210BPage/handouts/quadint.pdf>.

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