14 resultados para Rings (Algebra)
em Bulgarian Digital Mathematics Library at IMI-BAS
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2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.
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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006
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∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.
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The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group of linear automorphisms.
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In the present work are described the algorithms that generate all near-rings on finite cyclic groups of order 16 to 29.
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Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).
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We give a brief exposition of the history of the group rings and some their generalizations. Also we indicate some information of certain problems and results.
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This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.
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We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.
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2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.
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2000 Mathematics Subject Classification: Primary 13A99; Secondary 13A15, 13B02, 13E05.
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2000 Mathematics Subject Classification: 17A50, 05C05.
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MSC 2010: 46F30, 46F10
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2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.