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What is the relation between minimal polynomial of a matrix and of an algebraic integer?

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#linear-algebra #abstract-algebra #ring-theory #algebraic-number-theory
163
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Are Valuations on algebraic extensions of an henselian field unique?

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#abstract-algebra #field-theory #algebraic-number-theory #extension-field #valuation-theory
139
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Finding all ideals $T$ in number ring $\mathbb Z[\sqrt{-3}]$ s.t. $\langle 4 \rangle \subset T$.

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#abstract-algebra #ring-theory #algebraic-number-theory #ideals
215
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Compositum of unramified extension with a finite extension

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#algebraic-number-theory
29
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Interpretation of principal ideals in localisations of an order

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#number-theory #algebraic-number-theory
103
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Generalized Principal ideal theorem for ray class groups

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#algebraic-number-theory #class-field-theory
257
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Norm of elements in number field are rational

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#abstract-algebra #number-theory #field-theory #galois-theory #algebraic-number-theory
123
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Efficiently (by hand) determining principal prime ideals lying over a given prime in $\Bbb Z$. $\Bbb{Q}(\sqrt{5})$.

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#number-theory #algebraic-number-theory #prime-factorization
203
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Understanding the $p$-part of the discriminant of a totally real number field with a single prime above $p$

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#algebraic-number-theory #p-adic-number-theory #discriminant #ramification
40
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Powers of maximal ideal in Dedekind ring

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#algebraic-number-theory #maximal-and-prime-ideals #dedekind-domain
286
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Next book in learning Algebraic Number Theory

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#soft-question #algebraic-number-theory #book-recommendation #research
179
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Confused about the splitting of 2 in $\mathbb{Q}(i).$

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#abstract-algebra #algebraic-number-theory
63
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Showing integrality of a certain ring

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#commutative-algebra #algebraic-number-theory
744
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How come algebraic closure is not unique?

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#abstract-algebra #polynomials #field-theory #algebraic-number-theory
257
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Splitting primes and quadratic reciprocity.

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#number-theory #prime-numbers #proof-explanation #algebraic-number-theory

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