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Decomposition of the Steinberg group over local rings into involutions

Published online by Cambridge University Press:  17 April 2009

Ji Zhu Nan
Affiliation:
Department of Mathematics, Northeast Normal University, Chang Chun 130024, China
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Abstract

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We consider the stable Steinberg group St (R) over local rings. An element x is called an involution if x2 = 1. We prove that every element δ in St (R) is the product of at most 5 involutions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Ambrosiewicz, E., ‘Powers of set of involutions in linear group’, Demonstratio. Math 24 (1991), 311314.Google Scholar
[2]Dennis, R.K. and Vaserstein, L.N., ‘On a question of M. Newman on the number of commutators’, J. Algebra 118 (1988), 150161.Google Scholar
[3]Gustafson, W.H., ‘On products of involutions’, in Paul Halmos celebrating 50 years of Mathematics (Springer-Verlag, Berlin, Heidelberg, New York, 1991).Google Scholar
[4]Gustafson, W.H., Halmos, P.R. and Radjavi, H., ‘Products of involutions’, Linear Algebra Appl. 13 (1976), 157162.Google Scholar
[5]Hahn, A. and O'Meara, O.T., The classical groups and K-theory (Springer-Verlang, Berlin, Heidelberg, New York, 1989).Google Scholar
[6]Knuppel, F. and Nielsen, K., ‘SL (V) is 4-involutional’, Geom. Dedicata 38 (1991), 301308.CrossRefGoogle Scholar
[7]Milnor, J., Introduction to algebraic K-theory (Princeton University Press, Princeton, 1971).Google Scholar
[8]Silvester, J.R., Introduction to algebraic K-theory (Chapman and Hall, London, New York, 1981).Google Scholar
[9]You, H. and Nan, J.Z., ‘Decomposition of matrices into 2-involutions’, Linear Algebra Appl. 186 (1993), 235243.Google Scholar