In Cox's book "Primes of the form $x^2 + ny^2$", he proves that in a quadratic imaginary field $K$, if $\mathcal O$ is an order of conductor $f \in \mathbb Z$, we have that the class group ...
There are a number of concepts in model theory - often situated around Hrushovski's amalgamation method (see for instance http://math.univ-lyon1.fr/~wagner/nijmegen.pdf) - which are colorfully named: ...
Does there exist a Riemann surface corresponding to every field extension? Any other hypothesis needed?
My question is a doubt I had in the last point to the first answer to this MO question - "Algebraic" topologies like the Zariski topology? Can one associate a Riemann surface to any ...
I've heard of at least three slight modifications of the standard concept of field: meadow, which (according to this paper) is a commutative ring with unit equipped with a total unary operation ...
The terminology would suggest that a separable field extension is so because the resulting field extension has some sort of separable topology, and that a normal extension corresponds to one with a ...
In his very nice article Peter Roquette, History of valuation theory. I. (English summary) Valuation theory and its applications, Vol. I (Saskatoon, SK, 1999), 291--355, Fields Inst. Commun., ...