Novikov B. Comology of semigroups.

The thesis is devoted to investigation of semigroup cohomology and its applications. Properties of semigroups of cohomological dimension 1 are studied, in particular, the weakened Mitchell conjecture is proved. A new construction of partial cohomology is proposed, its cotriple presentation and relation to Eilenberg - MacLane cohomology is obtained. The Eilenberg - MacLane cohomology groups of some classes of semigroups are founded with the help of partial cohomology, and, in particular, the serie of counter-examples to the Mitchell conjecture is given. The using of partial cohomology for classification of the strongly primary algebras is proposed, new properties of the Brauer monoid are obtained.