Polyakova L. Homology of monoids

Object: homology of semigroups and monoids; aim: to develop methods of homology of monoids computation, to describe homological properties of free partially commutative monoids; research methods: methods of homological algebra, semigroup theory and graph theory; theoretical results: the 0-homology theory of semigroups and monoids is built, the connections of 0-homology and Eilenberg-MacLane homology are found; the resolutions for free partially commutative monoids are constructed and the Husainov Conjecture about homological dimension is proved; the codes of defect 3 are described and the properties of homological complexity of the code are investigated; degree of application: the results can be used in homological algebra and semigroup theory for further investigation of homology of monoids, in computer science for investigation of concurrency models, special courses can be based on the results.