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knsam
  • Member for 9 years, 5 months
  • Last seen more than a month ago
  • Kingston, ON
792 votes
1 answer
43k views

A proof for $\dim(R[T])=\dim(R)+1$ without prime ideals?

128 votes
6 answers
9k views

Why are the solutions of polynomial equations so unconstrained over the quaternions?

  • 62.7k
93 votes
8 answers
25k views

How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?

  • 1,419
86 votes
2 answers
12k views

Sheaf cohomology: what is it and where can I learn it?

  • 83k
84 votes
15 answers
180k views

What are the practical applications of the Taylor Series?

  • 1,495
72 votes
5 answers
7k views

Why should I care about adjoint functors

  • 4,520
65 votes
5 answers
8k views

Intuition for the Importance of Modular Forms

64 votes
5 answers
13k views

Help understanding Algebraic Geometry

  • 983
63 votes
6 answers
9k views

Similar matrices and field extensions

  • 631
61 votes
1 answer
2k views

When are nonintersecting finite degree field extensions linearly disjoint?

51 votes
6 answers
2k views

Is there a non-commutative ring with a trivial automorphism group?

51 votes
1 answer
7k views

An example of a division ring $D$ that is **not** isomorphic to its opposite ring

48 votes
2 answers
3k views

Is a finite group uniquely determined by the orders of its elements?

46 votes
5 answers
9k views

Simplicity of $A_n$

  • 2,724
46 votes
5 answers
20k views

Example of modules that are projective but not free; torsion-free but not free

  • 7,328
46 votes
5 answers
6k views

Consequences of Degree Theory

  • 16.5k
44 votes
4 answers
6k views

Is every embedded submanifold globally a level set?

43 votes
4 answers
7k views

Proving the snake lemma without a diagram chase

  • 83k
41 votes
6 answers
15k views

Efficiently finding two squares which sum to a prime

  • 674
41 votes
2 answers
2k views

Shortest irreducible polynomials over $\Bbb F_p$ of degree $n$

41 votes
3 answers
9k views

Use of Reduced Homology

40 votes
2 answers
2k views

A question on Taylor Series and polynomial

  • 2,720
37 votes
2 answers
6k views

"Standard" ways of telling if an irreducible quartic polynomial has Galois group C_4?

35 votes
3 answers
2k views

What does the topology on $\operatorname{Spec}(R)$ tells us about $R$?

  • 373k
33 votes
2 answers
16k views

A group $G$ with a subgroup $H$ of index $n$ has a normal subgroup $K\subset H$ whose index in $G$ divides $n!$

  • 409
33 votes
4 answers
11k views

Application of the Sylow Theorems to groups of order $p^2q$

  • 2,443
33 votes
1 answer
40k views

Elegant proofs that similar matrices have the same characteristic polynomial?

  • 18.3k
33 votes
3 answers
10k views

What is the difference between a variety and a manifold?

33 votes
3 answers
6k views

A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$

  • 3,235
32 votes
6 answers
7k views

A non-noetherian ring with noetherian spectrum

  • 10.9k
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