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Makoto Kato

I am neither a student nor a teacher of mathematics. Mathematics is my hobby. I am interested in algebraic number theory and algebraic geometry.

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23
Abelian categories and axiom (AB5)
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18
Is there a purely algebraic proof of the Fundamental Theorem of Algebra?
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15
Showing a homomorphism of a field algebraic over $\mathbb{Q}$ to itself is an isomorphism.
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12
Proving that $\mathbb{R^*}$ is not a cyclic group
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9
Discriminant of number field
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8
Compositum of abelian Galois extensions is also?
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7
If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
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7
Prerequisite reading for Weil's Basic Number Theory
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7
Find all subgroups of $\mathbb{Z}\times\mathbb{Z}$.
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7
True or false or not-defined statements
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6
Why $E$ is the algebraic closure of $K$?
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6
A Galois Group Problem
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6
Constructing a Galois extension field with Galois group $S_n$
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6
Theorems with an extraordinary exception or a small number of sporadic exceptions
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6
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
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6
The definition of a normal subgroup
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6
Every group has a subgroup of prime order?
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6
Does every ring with unity arise as an endomorphism ring?
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5
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
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5
Constructing a Galois extension field with Galois group $S_n$
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5
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
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5
The distance function is continuous.
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5
Interpreting the Cayley-Hamilton theorem
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5
How can I break up $z = \frac{5}{9+3i}$
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5
If $F\subseteq R \subseteq E$ where $E$ is an extension of $F$ and $R$ is an $F$-subspace, show that $R$ is a field.
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