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LIFTINGS OF THEELEMENTARY GROUP OVER ASSOCIATIVE RINGS

Published online by Cambridge University Press:  01 May 2000

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Abstract

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Let R be an associative ring with 1, and let I be a nilpotent two-sided ideal of R. Assume further that there exists z \in Z(R) such that z, z^2-1 \in R^*. Let m \in ℕ with m \geq 3. In this paper we describe all liftings of the elementary group{\tf="times-b"E}_m(R/I\,) to the general linear group{\tf="times-b"GL}_m(R) , i.e. all splittings of the natural projection{\tf="times-b"E}_m(R) + {\tf="times-b"M}_m(I\,) \rightarrow {\tf="times-b"E}_m(R/I\,) .

Type
Research Article
Copyright
2000 Glasgow Mathematical Journal Trust