Journal of Prime Research in Mathematics

# Matrix lie rings that contain an abelian subring

Evgenii L. Bashkirov
Department of Physics and Mathematics, Smolensk State University, Przhevalsky st. 4, Smolensk 214000 Russia.

$$^{1}$$Corresponding Author: bashkirov57@mail.ru

### Abstract

Let $$k$$ be a field and $$\overline{k}$$ an algebraic closure of $$k$$. The paper is devoted to the description of subrings of the Lie ring $$sl_{2}overline{k}$$ that contain an abelian subring which is a one-dimensional subspace of the $$k$$-vector space $$sl_{2}overline{k}$$.

#### Keywords:

Lie rings, lie algebras, semi-simple matrices, nilpotent matrices.