Abstract
The purpose of this paper is to develop an analogue to the theory of group extensions for Lie rings. Factor triple of a pair of Lie rings (L, A) is defined and used to construct extensions of A by L. This leads to Schreier's theorem for Lie rings. We also use the notion of factor triples to define the second cohomology group of (L, A) in the case where A is abelian and L acts on A.
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