Dudchenko I. Strongly connected quivers and A-full matrix algebras.

The thesis is devoted to the research of relations between different classes of rings, Fujita’s algebrs and strongly connected quivers by means of the theory of non-negative matrix. We have built Frobenius rings with the quiver Q, and the adjacency matrix [Q] of Q is (0, 1)-matrix and explored properties of these rings. We have proved that the quiver of every Fujita’s algebra is strongly connected and Fujita’s algebra has a multiplicative basis. We studied the ring’s properties of Fujita’s algebras. It is proved a criterion of isomorphism for simply laced strongly connected quivers without loopes with 2, 3 and 4 vertices. For these quivers it is counted their indices (the most positive eigen-vectors of their adjacency matrices) and eigen-vectors with these indices.