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Information × Registration Number 0211U001170, 0106U000630 , R & D reports Title Metric matrix problems and problems of group theory popup.stage_title Head Drozd Iurii Anatolyevich, Registration Date 21-01-2011 Organization Institute of mathematics NAS of Ukraine popup.description2 The theory of matrix problems and their application techniques is developed. The action of groups on bimodules and bimodule categories, the matrix problem for which representation with the trivial algebra endomorphisms form only one-parameter family is investigated. New methods in the theory of derived categories are developed, criteria for being "tame" and "wild" for the derived categories of local and two-point algebras and algebras with square-zero radical are obtained. Koszul duality for the standard module categories over quasi hereditary algebras is constructed. The wildness criteria for hypersurface singularities is found, which lead the study of Cohen-Macaulay types to the two-dimensional case only. Cubic rings and their ideals are described, as well as nodal algebra over a discrete valuation ring. A new method of classifying Cohen-Macaulay modules over a non-isolated surface singularities is developed, and the classification of Cohen-Macaulay modules over a wide class of such singularities is described. Weakly Dedekind groups are described. For groups with generalized minimality conditions the criteria to be chernikov is found. Almost quasi-Hamiltonian and meta-Hamiltonian groups are studied. The connections between the ring structure and its associated groups and Lie algebras are investigated. Wreath product construction through generators and relations is developed. Also locally almost rings are investigated. The structure of almost circular rings with almost additive group is described. Product Description popup.authors Бондаренко Віталій Віталійович Бондаренко Віталій Михайлович Волошин Денис Євгенович Сисак Ярослав Прокопович Черніков Микола Сергійович popup.nrat_date 2020-04-02 Close