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Information × Registration Number 0221U102666, 0116U003125 , R & D reports Title Development and applications of new methods in representation theory, abstract algebra and algebraic geometry popup.stage_title Head Drozd Yurii А., Доктор фізико-математичних наук Registration Date 08-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  Object of research: Cohen-Macaulay modules, categorical resolutions of singularities, representations of semigroups, structure theory of groups, cohomologies of groups, theory of near-rings. Aim of research: to develop new methods of investigation of Cohen-Macaulay and calculation of cohomologies of groups, to study representations of new classes of semigroups, to develop and apply the technic for construction of categorical resolutions of varieties, to investigate new classes of groups with factorizations and new classes of near-rings, to develop and implement algorithms for their classification. Methods of research: methods of representation theory, algebraic geometry, homological algebra, theory of categories, theory of groups and near-rings. New technic was developed for study of Cohen-Macaulay modules over non-isolated surface singularities, such modules are described over degenerate cusps, counter-example for the Schreier conjecute were constructed. A simplified resolutiwas on for calculation of cohomologies of finite abelian groups was constructed, cohomologies of irreducible lattices were calculated as well as cohomologies of all lattices over the Klein four-group. Cohen-Macaulay module were described over the singularities of type T44 and T36. The behaviour of stable categories and Auslander-Reiten quivers under rejection of bijective lattices over orders was studied. New classes of near-rings were studied and described. A new algorithm was developed for constructing local near-rings, the library of near-rings of small orders was created. Product Description popup.authors Bondarenko Vitalii Mykhailovych Gavran Volodymyr Semenovych Plakosh Andriana Ivanivna Raevska Iryna Yuriivna Raevska Maryna Yuriivna Sysak Yaroslav Prokopovych Tovpyha Oleksii Volodymyrovych popup.nrat_date 2021-02-08 Close