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Norm in algebraic number fields

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#algebraic-number-theory
189
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can anyone give a proof by definition: $11$ is prime in $ \mathbb{Z}[\sqrt{-5}] $

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#abstract-algebra #number-theory #algebraic-number-theory
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Prime ideals of the ring of integers of an algebraic number field

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#algebraic-number-theory #ideals #dedekind-domain
315
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Typo in the book or am I going crazy?

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#linear-algebra #algebraic-number-theory
39
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How to show that if $\gamma \alpha=0$ (mod $A$) then $\alpha = 0$ (mod $A$)

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#algebraic-number-theory #ideals
702
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Quotient ring of the ring of integers of an algebraic number field and its fraction field

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#algebraic-number-theory #ideals
64
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Can we tell if a number is prime by the number of its partition ?

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#number-theory #elementary-number-theory #algebraic-number-theory #analytic-number-theory
70
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Lattice with conditions

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#group-theory #algebraic-number-theory
505
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Eisenstein integers and applications to Diophantine equations

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#number-theory #algebraic-number-theory #diophantine-equations
163
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What is the 'Hom-description'?

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#abstract-algebra #number-theory #algebraic-number-theory #k-theory #algebraic-k-theory
1.3k
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Nice proof that $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain wrt absolute norm map

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#abstract-algebra #algebraic-number-theory
378
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What is a concrete example to demonstrate that $\mathcal{O}_{\mathbb{Q}(\sqrt{-19})}$ is NOT a norm-Euclidean domain?

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#algebraic-number-theory
574
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Why do we have to work to prove the surjectivity of the local Artin map (Serge Lang A.N.T., Chapter XI Theorem 3)

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#number-theory #algebraic-number-theory #class-field-theory
3.3k
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Motivation and examples for ramification

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#commutative-algebra #algebraic-number-theory #intuition #examples-counterexamples #motivation
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How to factor ideals in a quadratic number field?

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#abstract-algebra #algebraic-number-theory

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