Drozd-Koroleva O. Matrix problems over non-algebraically closed fields

The thesis is devoted to the expansion of the existing algorithms and results for matrix problems to the situation of problems over algebraically nonclosed fields. A reduction algorithm for bimodule problems over rings has been constructed, which generalizes the well-known algorithm of Kleiner-Roiter. From it the strengthened Brauer-Thrall conjecture for locally artin bimodules and for modules over artin algebras has been derived. The representations of weighed partially ordered sets have been considered. The reflection functors have been constructed for them and a criterion of representation finiteness has been obtained. The generalized bunches of chains and their representations have been introduced. A reduction algorithm and the combinatorics of strings and bands have been developed. A method of constructing all indecomposable representations from string and band data has been elaborated.