0
votes
0answers
7 views

Upper bound on cardinality of a field [migrated]

Is there an upper bound on the cardinality of a field? The "biggest" fields I know are the field of real numbers, or the field of complex numbers. Is there a field with cardinality greater than ...
2
votes
1answer
153 views

English translation of Steinitz 1910?

Does there exist an English translation of Steinitz' 1910 work "Algebraische Theorie der K├Ârper"? http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN002167042
0
votes
1answer
190 views

Is there a subfield $F$ of $\mathbb{R}$ such that $\mathbb{R}$ is a finite algebraic extension of $F$. [duplicate]

Possible Duplicate: Examples of algebraic closures of finite index The question is in the title. I can prove that if such field $F$ exist then the extension $\mathbb{R}/F$ cannot be of ...
5
votes
3answers
505 views

Octic family with Galois group of order 1344?

Does the octic, $\tag{1} x^8+3x^7-15x^6-29x^5+79x^4+61x^3+29x+16 = nx^2$ for any constant n have Galois group of order 1344? Its discriminant D is a perfect square, $D = ...