Algebraic Closure
Can someone give an example of a field F, which is not algebraicly
closed, but with the property that its algebraic closure has finite
dimension over F? I know that the real numbers have the property
(their algebraic closer is the complex numbers, which have dimension 2
over the reals), but are there any others?
.
Relevant Pages
- Re: ? def of complex number
... numbers are merely the next in a family of numbers beyond the reals. ... As the sign rises so does the dimension. ... requirements but the division clause of the field requirements. ... which includes unidirectional time as P1 which is also zero ...
(sci.math) - Re: Understanding the quotient ring nomenclature
... the next dimension as is going on in the ring quotient. ... Say we have the ring Z/, integers modulo 12. ... If fis a polynomial over the reals, ... Going off of this interpretation I would think that real numbers ...
(sci.math) - Re: Formal/Axiomatic Treatment of Units?
... of each dimension - length, mass, time, etc and a scalar measurement. ... dimensionaless quantities the reals. ... > is the unique additive-order isomorphism that takes 1 to the element ...
(sci.math) - Re: Understanding the quotient ring nomenclature
... Keywords: ideal, ring, quotient ring. ... for reals. ... are stuck in infinite dimension. ...
(sci.math) - Re: Understanding the quotient ring nomenclature
... build n dimensional spaces consistent with the ring requirements, ... infinite dimension, ... construction or is it more like a hindsight type of thing where a given ... many insist upon constructing the polysign numbers from the reals. ...
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