Main directions of investigations:
- Linear algebra, theory of matrices
over rings. The structure of matrices over certain classes of finitely generated principal
ideal rings, in particular,
the polynomial rings, principal ideal
rings, adequate rings
etc. is studied in such aspects:
- different
types of matrix equivalence and their finite sets, construction of simpler forms, in particular canonical, relative to such equivalences;
- on
the basis of there forms the methods of matrix factorization are developed; the matrix equations were solved.
- Finite-dimensional Lie algebras. Investigation of structural
properties of nonconjugate subalgebras
of the finite-dimensional Lie algebras as well as its applications for
solving problems of theoretical and mathematical physics.
- Topological graph theory. Studying embeddings and
immersions of graphs in two-dimensional surfaces.