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Field Theory and Galois

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Explanations 1

Recall that the complex numbers are numbers of the form a+bia+bia+bi where a,b∈Ra, b \in \mathbb{R}a,b∈R, i.e. aaa and bbb are real numbers, and the symbol iii satisfies the equ…
By Mendel Cyprys

Problems 4

Which of the following objects is NOT universal (in the sense of universal properties) with respect to the given property?
If E1,E2E_1,E_2E1,E2 are subfields of a larger field FFF, with finite degrees [F:E1],[F:E2]<∞[F:E_1],[F:E_2]<\infty[F:E1],[F:E2]<∞, must the intersection E1∩E2E_1\cap E_2E1…
Let K(T)K(T)K(T) be the rational function field over a base field KKK, and let f∈K(T)f\in K(T)f∈K(T) be a non-constant element (intuitively, a "function" in the variable TTT). W…
Let zzz be a transcendental element (over the base KKK) in a field extension F/KF/KF/K. Over which of the following subfields of FFF must zzz necessarily be transcendental?