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Prime Extensions of Skew Fields

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Abstract

Prime extensions are extensions that have no nontrivial intermediate fields. In this chapter, it is explored what types of them are possible. It is shown that any prime extension is of one of the three types outer central, inner plain or outer plain. Moreover, for type outer central it is shown that L/K is prime iff Z(L)/Z(K) is, and for type inner plain that L/K is prime iff Z(K)/Z(L) is.
Chapter 9
Prime Extensions
of Skew Fields1
Jan Treur
https://www.researchgate.net/profile/Jan_Treur
j.treur@vu.nl
1 In: Treur, J., A Duality for Skew Field Extensions, Ch 9, pp. 89-92. Utrecht University,
Department of Mathematics, Ph.D. Thesis, 1976.
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