Chernousova J. Tiled orders and their ideals

The thesis is devoted to the study of tiled orders and their ideals, factor rings modulo the ideals being quasi-Frobenius. All reduced cyclic Gorenstein tiled orders are described. It is proved that in an indecomposable reduced semiperfect right noetherian semiprime semidistributive ring there is a countable set of ideals, factor rings modulo the ideals being quasi-Frobenius. For every reduced tiled order, Frobenius factor rings with identical Nakayma's permutation are constructed. All ideals, factor rings modulo them being quasi-Frobenius, of tiled orders with exponent matrix being the Cayley table of elementary abelian 2-group are characterized. We found a connection between permutations of the Gorenstein tiled order.