Allowable diagrams for purely inseparable field extensions
Abstract: We define a diagram associated with a purely inseparable field extension of finite exponent. We show that, under this definition, for any given field extension the shape of its diagram is unique. Thus our diagram improves the diagram defined by Sweedler in [2, p. 402].
In §2 we define an ``allowable'' shape for a diagram. Given any ``allowable'' shape for a diagram representing a finite field extension, we construct a field extension whose diagram has that shape.
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Keywords: Purely inseparable, diagram of a field extension
Article copyright: © Copyright 1973 American Mathematical Society