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Homology of multiplicative Lie rings |
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| Authors: | A Bak G Donadze |
| Institution: | a Department of Mathematics, University of Bielefeld, P. O. Box 100131, 33501 Bielefeld, Germany b A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Alexidze St. 1, 0193 Tbilisi, Georgia c Departamento de Álgebra, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain |
| Abstract: | Two homology theories of multiplicative Lie rings are constructed, studied and compared with the usual homology theories of groups and Lie rings. Central extensions of multiplicative Lie rings are introduced. It is shown that the Steinberg multiplicative Lie ring of a ring is the direct product of the Steinberg group (viewed as a multiplicative Lie ring under the commutator bracket) and the Steinberg Lie ring. |
| Keywords: | 18G10 18G50 |
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