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.
-  Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871
-  Moss Eisenberg Sweedler, Structure of inseparable extensions, Ann. of Math. (2) 87 (1968), 401–410. MR 0223343, https://doi.org/10.2307/1970711
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Keywords: Purely inseparable, diagram of a field extension
Article copyright: © Copyright 1973 American Mathematical Society