Deformations of a two-generator purely inseparable field of exponent 1

Abstract

This paper gives a discussion of the algebraic deformations of a two-generator purely inseparable field of exponent 1, this being the simplest field having noncommutative deformations. It gives a necessary condition for a 2-cocycle to be integrable and, if it is allowed to adjoin a single separable element to the groundfield, also a sufficient condition for a 2-cocycle to be integrable. The method used is to study certain skew symmetric biderivations associated with the field.