Vol. 83, No. 1, 1979

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Splitting and modularly perfect fields

James K. Deveney and John Nelson Mordeson

Vol. 83 (1979), No. 1, 45–54
Abstract

Let K be a field of characteristic p0. A field extension L∕K is said to split when there exist intermediate fields J and D of L∕K where J is purely inseparable over K, D is separable over K and L = J KD. K is modularly perfect if [K : Kp] p. Every finitely generated extension of a modularly perfect field splits. This paper develops criteria for an arbitrary extension L∕K to split and presents an example of an extension of a modularly perfect field which does not split. Necessary and/or sufficient conditions are also developed for the following to hold for an extension L∕K: (a) L∕K splits for every intermediate field L; (b) L∕K is modular for every intermediate field L; (c) L∕Lsplits for every intermediate field L; (d) L∕Lis modular for every intermediate field L.

Mathematical Subject Classification 2000
Primary: 12F15
Milestones
Received: 27 October 1973
Published: 1 July 1979
Authors
James K. Deveney
John Nelson Mordeson