Makoto Kato

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Classification of prime ideals of $\mathbb{Z}[X]$

abstract-algebra commutative-algebra ideals prime-ideals asked Jul 24, 2012 at 9:38

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68 votes

Is memory unimportant in doing mathematics?

soft-question learning asked Nov 17, 2012 at 1:44

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68 votes

Is an automorphism of the field of real numbers the identity map?

abstract-algebra field-theory real-numbers asked Jul 22, 2013 at 12:00

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44 votes

Are the exercises necessary to understand the subject of a mathematical textbook?

soft-question learning asked Jun 28, 2012 at 2:29

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43 votes

Mnemonic for the fact that a right(left) adjoint functor preserves limits(colimits)

category-theory adjoint-functors asked Jan 5, 2013 at 15:55

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33 votes

Do native speakers distinguish well the pronunciations of "L" and "R"?

pronunciation phonetics consonants asked Oct 12, 2015 at 0:50

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33 votes

Unramification of a prime ideal in an order of a finite Galois extension of an algebraic number field

algebraic-number-theory asked Aug 17, 2012 at 6:22

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27 votes

Differentiable manifolds as locally ringed spaces

differential-geometry sheaf-theory asked Oct 30, 2012 at 21:16

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27 votes

"No more Hiroshima" or "No more Hiroshimas"

grammatical-number proper-nouns negative asked Jan 14, 2015 at 10:52

ell.stackexchange.com

27 votes

A natural proof of the Cauchy-Schwarz inequality

functional-analysis inequality asked Jul 5, 2013 at 5:31

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Top Answers

Is an automorphism of the field of real numbers the identity map?

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Abelian categories and axiom (AB5)

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Is there a purely algebraic proof of the Fundamental Theorem of Algebra?

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Verifying that the ideal $(x^3-y^2)$ is prime

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Constructing a Galois extension field with Galois group $S_n$

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Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group

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An element of a group $G$ is not conjugate to its inverse if $\lvert G\rvert$ is odd

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Spivak's proof of Inverse Function Theorem

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Nontrivial theorems with trivial proofs

mathoverflow.net

How can I prove formally that the projective plane is a Hausdorff space?

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Showing a homomorphism of a field algebraic over $\mathbb{Q}$ to itself is an isomorphism.

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Why a polynomial is solvable by radicals iff its Galois group is solvable, when $char(F)=0$?

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Find all subgroups of $\mathbb{Z}\times\mathbb{Z}$.

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Compositum of abelian Galois extensions is also abelian?

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Find the number of non-zero squares in the field $Zp$

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Prove $\sin x$ is uniformly continuous on $\mathbb R$

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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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How are tangent spaces defined through equivalence classes of curves?

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Finitely generated modules in exact sequence

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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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how to show that power series is analytic inside the radius of convergence?

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Why are topological spaces interesting to study?

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Theorems with an extraordinary exception or a small number of sporadic exceptions

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Why is the tensor product important when we already have direct and semidirect products?

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Morphism of Affine Algebraic Variety

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An automorphism of the field of $p$-adic numbers

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Sheafification of a presheaf through the etale space

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Proofs of the properties of Jacobi symbol

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Showing that a Sylow subgroup of a group of order $p^{2}q$ is normal.

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Example of nonabelian group with all proper subgroups normal

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