Babych V. Category methods in bimodule problem theory and ring theory

The thesis is devoted to the decision of representation type finiteness problem for some class of bimodule problems over the ring of power series in one variable over an algebraically closed field and some questions of factorization in associative rings. The bimodule problems of finite representation type from the considered class are described. The complete list of critical bimodule problems from the considered class is received. The fundamental groups of bimodule problems from the considered class are described. Quadratic forms of two-point bimodule problems from the considered class are explored on weak non-positivity. The module-theoretic characterization is given for factorization of elements in rings.