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1. Field (mathematics)

   Linked via "fundamental theorem of Galois theory"

   Transcendental Extension: An element $\alpha \in E$ is transcendental over $F$ if it is not algebraic over $F$.
   The study of algebraic extensions is deeply intertwined with the construction of roots of unity\ and the solvability of polynomial equations\, a concept formalized by the fundamental theorem of Galois theory\.
   Subfields and Prime Fields