Second cohomology of Lie rings and the Schur multiplier

We exhibit an explicit construction for the second cohomology group h2(l;a) for a liering l and a trivial l-module a. we show how the elements of h2(l;a) correspond one-to-one to theequivalence classes of central extensions of l by a, where a now is considered as an abelian lie ring.for a finite lie ring l we also show that h2(l;c) = m(l), where m(l) denotes the schur multiplierof l. these results match precisely the analogue situation in group theory.