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What is known about the minimal absolute value in $\mathbb{Z}[\zeta_n]\setminus\{0\}$?

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#abstract-algebra #roots-of-unity #cyclotomic-fields #algebraic-integers
43
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On the proof of: If $0<\frac{|χ(g)|}{χ(1)}<1$ then $\frac{χ(g)}{χ(1)}\notin\overline{\mathbb{Z}}$

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#representation-theory #characters #algebraic-integers
76
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Product of almost all Galois conjugates

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#matrices #galois-theory #algebraic-number-theory #algebraic-integers
103
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Upper bound on number of algebraic integers of degree $\leq d$

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#number-theory #algebraic-number-theory #algebraic-integers
77
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The notion of "units" is independent of the base algebraic integer ring.

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#abstract-algebra #algebraic-number-theory #integral-extensions #algebraic-integers
51
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Find all units in the ring $\Bbb Z[\omega]$ where $\omega$ is the primitive $p^{th}$ root of unity.

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#abstract-algebra #ring-theory #algebraic-number-theory #cyclotomic-fields #algebraic-integers
36
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Sums of powers and algebraic integers

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#number-theory #algebraic-integers
207
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The house of an algebraic number

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#algebraic-number-theory #diophantine-approximation #algebraic-integers
135
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Problem relating $p$-defect zero characters with their values on a field of characteristic $p$

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#group-theory #finite-groups #characters #algebraic-integers
58
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Algebraic number theory proof question

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#algebraic-number-theory #finitely-generated #algebraic-integers
119
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Algebraic number theory - finiteness of quotient

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#algebraic-number-theory #group-isomorphism #finitely-generated #quotient-group #algebraic-integers
91
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Proving quotient of $\mathcal{O}_K $ with ideal $I$ is finite.

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#algebraic-number-theory #ideals #quotient-group #algebraic-integers
359
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Proof of Dedekind-Kummer theorem

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#algebraic-number-theory #maximal-and-prime-ideals #quotient-group #ring-isomorphism #algebraic-integers
69
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Symmetric Expressions in Roots of Polynomial with Coefficients in Integral Domain

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#field-theory #galois-theory #algebraic-integers
222
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Can every transcendental number be expressed as the infinite sum of a quotient of two polynomials?

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#sequences-and-series #real-numbers #transcendental-numbers #algebraic-integers

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