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22 votes
1 answer
1k views

Why is the Hessian of an irreducible polynomial not zero?

18 votes
1 answer
630 views

The polynomial whose roots are all real

17 votes
1 answer
1k views

Irreducible components of topological space

16 votes
3 answers
1k views

Question about UFD

14 votes
2 answers
2k views

Must $k$-subalgebra of $k[x]$ be finitely generated?

14 votes
2 answers
3k views

Irreducible polynomial modulo every prime?

12 votes
3 answers
2k views

Are the determinantal ideals prime?

11 votes
2 answers
3k views

Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma

9 votes
1 answer
1k views

The Ring of Cauchy Sequences

8 votes
2 answers
2k views

How do I prove a scheme is connected?

8 votes
1 answer
543 views

Question about Zariski topology

8 votes
2 answers
1k views

Why we need to add the notion of "separated" to the notion of variety?

8 votes
1 answer
973 views

Irreducible polynomial over an algebraically closed field

7 votes
3 answers
191 views

Every element is radical in a field extension.

6 votes
1 answer
412 views

The product of two spectral spaces

6 votes
2 answers
340 views

a problem about binomial coefficients sum

6 votes
1 answer
136 views

Reference about $k$-algebra isomorphism of $k[x_1,\ldots,x_n]$

6 votes
1 answer
1k views

Going down theorem fails

6 votes
1 answer
99 views

An inequality question about $x\ln x+x^2$.

5 votes
1 answer
335 views

Examples of abelian group with some property

5 votes
1 answer
611 views

Must the projective closure of a closed subset of affine space have points at infinity?

5 votes
1 answer
719 views

Failures of Nakayama's lemma or Krull theorem

5 votes
1 answer
163 views

Is $f$ reduced if and only if the derivations $\gcd(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})=1$ under some conditions?

5 votes
1 answer
142 views

Is this module finitely generated?

4 votes
1 answer
486 views

A number is square in F_p for every prime p [duplicate]

4 votes
2 answers
215 views

Infinite many curves passing through finite points?

4 votes
1 answer
190 views

What is a statement?

4 votes
3 answers
2k views

Determine the centre of a circle

4 votes
1 answer
46 views

For what kind of a subset its sums equal $\mathbb{R}^4$

4 votes
1 answer
2k views

Subfields of the field of complex numbers with finite index rather than the real number field [duplicate]