Bronitska N. The global dimension of semiperfect rings

The dissertation is devoted to the learning of tiled orders of width two and their global dimensions. The work studies the way of calculation of global dimensions of some types of rings and tiled orders. are the building of serial Artinian rings, which satisfied the conditions of the theorem Gustafson (going from tiled orders of width 1) and tiled orders of width two with the biggest global dimension (using methods of the Gustafson's article) and building of countable sets of Gorenstein orders, index of which coincides with width two. The methods of right serial quivers prove the top limits of Loewy length for Artinian rings of finite global dimension. The methods for calculation of global dimension of tiled orders of width two are indicated. It is proved that if a Noetherian indecomposable ring has infinite global dimension so it is a prime SPSD-ring with nonzero Jacobson radical, in other words, tiled order. Tiled order has a classical ring of fractions and can have both infinite and finite global dimension. It is proved that in classical ring of fractions there is up to isomorphism, only a finite number of tiled orders of finite global dimension.