Shvyrov V. Properties of the serial rings

The structural properties of the noetherian serial rings, semiprime serial rings and serial rings with Krull dimension are investigated. We consider the connections between the ideals of the upper triangular matrices ring, Kupisch series of serial rings and Catalan's numbers. The principal modules over the serial ring and chains of submodules principal modules are learning. Also we obtained the structural results for the semiprime left noetherian right serial rings. We investigate the properties of the serial rings with Krull dimension and minors over such rings. Krull dimension of piecewise noetherian serial rings less or equal one are proved. We research connections between permissible sequences and Catalan's numbers.