Bilavska S. Stable range and connection rings theory and modules

The thesis is devoted to the calculation of a stable range different classes of a ring, partially the next classes of ring an adequate ring, an always adequate ring and also generalization stable ring of a regular ring and an elementary divisor ring. It is establish a connection an adequate ring with a clean ring, a neat ring and an exchange ring. There are discribe a finite homomorphic image of an adequate ring. There are describe a new classes of a non-commutative elementary divisors domain. Using a new notions of an almost prime submodule and dr-prime one-side ideal are obtain modular and non-commutative generalization of Cohen's theorem.