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What does “linearly disjoint” mean for abstract field extensions?

All definitions I've seen for the statement "$E,F$ are linearly disjoint extensions of $k$" are only meaningful when $E,F$ are given as subfields of a larger field, say $K$. I am happy with the ...
198 views

Decomposition result for multivariate polynomial

Let $k$ be a positive integer greater than $1$ and suppose that $F \in \mathbb{Z}[x_{1}, \ldots, x_{k}]$. Can we always find a natural number $n(k)$ and $f_{1}, \ldots f_{n(k)} \in \mathbb{Z}[x]$ ...
2k views

intuitionistic interpretation of classical logic

Basically intuitionistic logic is classical logic minus the law of the excluded middle, i.e. $\neg A\vee A$ is not necessarily valid for all formulas. So I would take this to mean that classical logic ...
8k views

Origins of Mathematical Symbols/Names

I'm not sure if this has been asked. I'll explain the question by an example. Fields are often denoted by the letter k, which comes from the German word Körper, meaning body (like corpse, corporeal). ...
3k views

Why is the decomposition theorem awesome?

I saw the statement of the decomposition theorem for perverse sheaves sometime ago. I know that (modulo most of the details) it implies some big theorems in algebraic geometry and gives new proofs for ...
7k views

Does anyone have an opinion on Alain Badiou's use of set theory? Is there anything interesting mathematically there? Also could anyone shed any light on the comment in the Wikipedia article link text ...
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Is it possible to capture a sphere in a knot?

You and I decide to play a game: To start off with, I provide you with a frictionless, perfectly spherical sphere, along with a frictionless, unstretchable, infinitely thin magical rope. This rope ...
330 views

name for “solid” subset of a partially ordered set?

For P a partially ordered set, let S be a subset of P such that if: a,c\in S and b\in P and a<=b<=c then b\in S Is there a name for a subset with this property? The term "dense" subset is ...

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