Vol. 52, No. 2, 1974

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The nonminimality of the differential closure

Maxwell Alexander Rosenlicht

Vol. 52 (1974), No. 2, 529–537
Abstract

The differential closure of a given ordinary differential field k is characterized to within (differential) k-isomorphism as a differentially closed (differential) extension field k of k which is k-isomorphic to a subfield of any differentially closed extension field of k. It has been conjectured that, in analogy to the cases of the algebraic closure of a field and the real closure of an ordered field, the differential closure of any differential field k is minimal, that is, not k-isomorphic to a proper subfield of itself. The conjecture is here shown to be false.

Mathematical Subject Classification 2000
Primary: 12H05
Secondary: 02H15
Milestones
Received: 7 June 1973
Published: 1 June 1974
Authors
Maxwell Alexander Rosenlicht