## Free color Lie super-rings.(English. Russian original)Zbl 0744.17033

Sov. Math. 35, No. 10, 42-44 (1991); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 10(353), 46-49 (1991).
The author proves analogs of the theorems of E. Witt and A. I. Shirshov for color Lie superalgebras. Namely, he proves the following results: (i) Any Lie superalgebra (or Lie $$p$$-superalgebra) of at most countable rank over a field of characteristic $$\neq 2,3$$ can be embedded into a Lie superalgebra (or $$p$$-superalgebra) with two generators over the same field; (ii) Let $$K$$ be a commutative domain over which all projective modules are free, $$L$$ be the free $$K$$-operator color Lie ($$p$$-) super- ring and $$B$$ be an isolated $$G$$-homogeneous subring of $$L$$. If $$B$$ is a direct summand of the $$K$$-module $$L$$ then $$B$$ is a free $$K$$-operator color Lie ($$p$$-) super-ring.
There is also the analog of P. M. Cohn’s criterion (for identical relations among left normed monomials in Lie rings) for free color Lie super-rings.

### MSC:

 17B70 Graded Lie (super)algebras 17A70 Superalgebras