Galapchuk S. Gorenstein quivers

The thesis is devoted to research of Gorenstein quivers, particularly, Gorenstein quivers, which have no more than 8 vertices, are investigated. For all Gorenstein quivers, which have no more than 7 vertices, it is found at what values of parameters they are quivers for given Gorenstein matrix. All Gorenstein quivers, which have no more than 7 vertices, are represented graphically. It is investigated on primitivity and imprimitivity adjacency matrices of Gorenstein quivers, which have no more than 8 vertices; their characteristic polynoms are obtained. It is found formulas, which gave possibility to set adjacency matrices of Gorenstein quivers of cyclic Gorenstein matrices up to the 8th order inclusive. All integer indices of Gorenstein quivers are obtained. Indices of imprimitivity adjacency matrices of cyclic Gorenstein quivers are found. Gorenstein criterion of reduced (0,1)-orders is obtained by means of ordinal degrees of partially ordered sets; all Gorenstein quivers which respond (0,1)-ordersare described.