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What are the different subjects in number theory to do research?

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#number-theory #elementary-number-theory #algebraic-number-theory #analytic-number-theory #ergodic-theory
96
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Coset representatives in the quotient of ring of integers

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#number-theory #field-theory #algebraic-number-theory #ideals
113
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Calculating the minimal polynomial of linear combinations of numbers

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#algebraic-number-theory
1.6k
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What is the difference between algebraic number theory, arithmetic geometry and diophantine geometry?

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#algebraic-geometry #soft-question #algebraic-number-theory #arithmetic-geometry
1.4k
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Maximal unramified extension of p-adic numbers

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#number-theory #algebraic-number-theory
60
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Set of $K$-primes over $p$ bijective with double quotient

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#algebraic-number-theory #prime-factorization #quotient-spaces
385
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Visualize ideals in number fields

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#number-theory #algebraic-number-theory #integer-lattices #geometry-of-numbers
876
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Galois group of $\mathbb{Q}_{p}$ over $\mathbb{Q}$?

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#galois-theory #algebraic-number-theory
920
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correspondence between totally, tamely ramified extension and value groups

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#algebraic-number-theory
579
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Why is a Nonzero Ideal of $\mathcal{O}_K$ Free of Rank $n$?

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#abstract-algebra #modules #algebraic-number-theory #ideals #free-modules
1.6k
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Existence of Solution to Generalized Pell's Equation

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#number-theory #elementary-number-theory #algebraic-number-theory #diophantine-equations #pell-type-equations
799
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Example of a noetherian domain which is neither Dedekind domain nor UFD?

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#abstract-algebra #ring-theory #commutative-algebra #algebraic-number-theory
173
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Corollary of Proposition 11 in Lang's Algebraic Number Theory

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#number-theory #algebraic-number-theory #maximal-and-prime-ideals #galois-extensions
78
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How to find the prime ideals of $\mathbb{Z}[i]$ using the associated map of spectra?

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#algebraic-geometry #ring-theory #algebraic-number-theory
273
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How is the Artin map defined for ramified extensions?

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#abstract-algebra #algebraic-number-theory #class-field-theory

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