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Minimal of Ring Theory for Field/Galois theory.

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#ring-theory #soft-question #field-theory
99
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Prove that the following set is a field

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#abstract-algebra #polynomials #proof-writing #field-theory #euclidean-algorithm
531
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Is every simple radical extension containing a primitive nth root of unity cyclic?

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#field-theory #galois-theory
417
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Any field that contains the integers contains the rationals as a subfield (Analysis proof)

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#real-analysis #field-theory #group-isomorphism
187
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Does every ordered divisible abelian group admit an expansion (and how many) to an ordered field?

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#field-theory #real-numbers #ordered-fields #ordered-groups #divisible-groups
4.3k
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Every irreducible polynomial over a finite field is separable

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#abstract-algebra #field-theory #finite-fields
235
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Where does $\pi$ of the class number formula come from?

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#field-theory #algebraic-number-theory #riemann-zeta #zeta-functions
246
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What can we say about class number of a number field using class number formula?

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#field-theory #algebraic-number-theory #riemann-zeta #zeta-functions
428
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Field automorphism over $\mathbb Q$ not mapping conjugate pairs

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#field-theory #galois-theory #rational-numbers
226
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number of not identically zero functions

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#linear-algebra #abstract-algebra #functions #ring-theory #field-theory
142
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Computing minimal polynomial

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#abstract-algebra #field-theory #galois-theory
104
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Bijection between filters and ideals

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#ring-theory #field-theory #filters
594
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Decompose tensor product of fields into direct product of domains

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#abstract-algebra #commutative-algebra #field-theory #extension-field #tensor-products
377
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How do you define the multiplication operation for a field extension?

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#abstract-algebra #field-theory
56
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Value of $L(1,\chi)$ when $\chi$ is defined via ramification of primes

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#number-theory #field-theory #prime-numbers #algebraic-number-theory #legendre-symbol

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