Makoto Kato

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


281 Answers

newest activity votes
23
Abelian categories and axiom (AB5)
18
Is there a purely algebraic proof of the Fundamental Theorem of Algebra?
15
Showing a homomorphism of a field algebraic over $\mathbb{Q}$ to itself is an isomorphism.
12
Proving that $\mathbb{R^*}$ is not a cyclic group
9
Discriminant of number field
8
Compositum of abelian Galois extensions is also?
7
Prerequisite reading for Weil's Basic Number Theory
7
True or false or not-defined statements
7
Find all subgroups of $\mathbb{Z}\times\mathbb{Z}$.
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 $d$
6
Does every ring with unity arise as an endomorphism ring?
6
Every group has a subgroup of prime order?
6
The definition of a normal subgroup
6
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
6
Theorems with an extraordinary exception or a small number of sporadic exceptions
6
Constructing a Galois extension field with Galois group $S_n$
6
A Galois Group Problem
6
Why $E$ is the algebraic closure of $K$?
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.
5
How can I break up $z = \frac{5}{9+3i}$
5
Interpreting the Cayley-Hamilton theorem
5
The distance function is continuous.
5
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
5
Constructing a Galois extension field with Galois group $S_n$
5
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
4
On theorem 15.4 of Matsumura
4
$x^{6}+30x^{5}-15x^{3}+6x-120$can't be written as products of two polynomials of rational coefficients and positive degrees.
4
Prove that a group G such that every element $g \in G$ satisfies the equality $g^2 = 1_G$ is abelian
4
How can I prove formally that the projective plane is a Hausdorff space?
4
Closed points of a scheme correspond to maximal ideals in the affines?
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