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15
166
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Can a field be canonically reconstructed from its multiplicative group?

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#abstract-algebra #vector-spaces #field-theory #abelian-groups #adjoint-functors
233
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Determine if the following extensions are normal

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#abstract-algebra #field-theory #galois-theory
510
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Dimension of centraliser of an $n \times n$ matrix is atleast n.

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#linear-algebra #matrices #field-theory #jordan-normal-form
44
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A Conjecture about the $K$-automorphisms of a field $L$.

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#abstract-algebra #group-theory #polynomials #field-theory #galois-theory
1.9k
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Constructing a field with exactly $81$ elements

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#abstract-algebra #number-theory #field-theory #ideals
73
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Product of values of the derivative of a polynomial at its roots

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#field-theory #irreducible-polynomials
667
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How is the integers modulo p a finite field.

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#field-theory
1.1k
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Are the real numbers the unique Dedekind-complete ordered set?

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#abstract-algebra #logic #field-theory #order-theory #real-numbers
1k
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Field that properly contains the field of complex numbers

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#abstract-algebra #field-theory
97
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If $\bar{k}\supseteq R\supseteq k$, then $R$ is a field?

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#abstract-algebra #field-theory
48
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$\sqrt{a-b\sqrt{c}} \in \mathbb Q(\sqrt{a+b\sqrt{c}})$

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#abstract-algebra #field-theory #extension-field
32
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An algebraic extension of degree 3

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#abstract-algebra #field-theory #extension-field
977
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Dimension of the vector space $\mathbb{Q}(\sqrt{3}, \sqrt{5}, \sqrt{11})$ over $\mathbb{Q}$

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#vector-spaces #field-theory
1.5k
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Understanding subfield test ( intuitive )

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#abstract-algebra #group-theory #ring-theory #field-theory #intuition
51
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Find a field $F$ such that $[F : \mathbb{Q}] = 3$ and $F \ne \mathbb{Q }(\sqrt[3]{a}), \forall a \in \mathbb{Q}$

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#field-theory #extension-field

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