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Information × Registration Number 0212U004174, 0107U000361 , R & D reports Title Elaboration of theoretical ring and group investigation methods for the factorization and classification of matrices over finitely-generated principal ideal rings and investigation of structural properties of finitely-dimensional Li algebras. popup.stage_title Head Petrychkovych Vasyl, Fedorchuk Vasyl, Registration Date 31-01-2012 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 The expressions for all monic divisors and common divisors of the polynomial matrices over arbitrary field with the given canonical diagonal forms are established. These divisors are found under the conditions of parallelism of the corresponding factorizations of matrices to the factorizations of their canonical diagonal forms. The method of constructing of block triangular and block diagonal factorizations of corresponding block matrices over a principal ideal domains is developed. The forms of matrices over polynomial rings and over rings of finitely generated principal ideals with respect to semiscalar equivalent, block diagonal equivalent, similar and other transformations are constructed. The classification of all non-conjugate low-dimensional subalgebras of the Lie algebra of the Poincare group P(1,4) into isomorphism classes of subalgebras are performed, as well as the invariant operators for all subalgebras of dimensions up to four of this Lie algebra are constructed. The algebraical and topological properties of the topological semigroup of finite partial bijections of an infinite set and of the topological extensions of semigroups are investigated. Product Description popup.authors Джалюк Н.С. Ладзоришин Н.Б. Павлик К.П. Петричкович В.М. Прокіп В.М. Романів А.М. Федорчук В.І. Федорчук В.М. Шаваровський Б.З. Щедрик В.П. popup.nrat_date 2020-04-02 Close