High Quality Content by WIKIPEDIA articles! In mathematics, more specifically in the area of modern algebra known as field theory, the primitive element theorem or Artin's theorem on primitive elements is a result characterizing the finite degree field extensions that possess a primitive element. More specifically, the primitive element theorem characterizes those finite degree extensions Esupseteq F such that there exists alphain E with E = F[ ] = F( ). According to a history of abstract algebra, the status in Galois theory, and the interpretation of the theorem, changed with the formulation of the theory of Emil Artin, around 1930. From the time of Galois, the role of primitive elements was to represent a splitting field as generated by a single element. This (arbitrary) choice of such an element was bypassed in Artin's treatment. At same time, considerations of construction of such an element receded: the theorem becomes an existence theorem.

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