![Rings of constants of the form k[f]](http://s1.studyres.com/store/data/021729650_1-3a6201c0eec615e02140355abcc4b661-300x300.png)
Separability
... Even if our main objects of study—rings of algebraic integers in number fields—all live in characteristic zero, we have a great interest in considering the case of positive characteristic. The reason is as follows. If A✓ B is an extension of say number rings— for example could B be the integtral clo ...
... Even if our main objects of study—rings of algebraic integers in number fields—all live in characteristic zero, we have a great interest in considering the case of positive characteristic. The reason is as follows. If A✓ B is an extension of say number rings— for example could B be the integtral clo ...
06 fields I - Math User Home Pages
... If k[α] ≈ k[x], then, for example, the various powers of α are linearly independent over k, and k[α] is infinitedimensional as a k-vectorspace. And there is no polynomial P (x) ∈ k[x] such that P (α) = 0. Especially in the simple situation that the k-algebra A is a field, such elements α with k[α] ≈ ...
... If k[α] ≈ k[x], then, for example, the various powers of α are linearly independent over k, and k[α] is infinitedimensional as a k-vectorspace. And there is no polynomial P (x) ∈ k[x] such that P (α) = 0. Especially in the simple situation that the k-algebra A is a field, such elements α with k[α] ≈ ...
The Fundamental Theorem of Algebra - A History.
... History of Abstract Algebra, Israel Kleiner, Birkhäuser (2007), page 12]. There are proofs which are mostly algebraic, but which borrow result(s) from analysis (such as the proof presented by Hungerford). However, if we are going to use a result from analysis, the easiest approach is to use Liouvill ...
... History of Abstract Algebra, Israel Kleiner, Birkhäuser (2007), page 12]. There are proofs which are mostly algebraic, but which borrow result(s) from analysis (such as the proof presented by Hungerford). However, if we are going to use a result from analysis, the easiest approach is to use Liouvill ...
