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

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

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

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

What are the practical applications of the Taylor Series?

Why should I care about adjoint functors

Intuition for the Importance of Modular Forms

Help understanding Algebraic Geometry

Similar matrices and field extensions

When are nonintersecting finite degree field extensions linearly disjoint?

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

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

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

Simplicity of $A_n$

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

Consequences of Degree Theory

Is every embedded submanifold globally a level set?

Proving the snake lemma without a diagram chase

Efficiently finding two squares which sum to a prime

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

Use of Reduced Homology

A question on Taylor Series and polynomial

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

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

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

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

Elegant proofs that similar matrices have the same characteristic polynomial?

What is the difference between a variety and a manifold?

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

A non-noetherian ring with noetherian spectrum