【摘 要】
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Consider the stable Steinberg group St(K) over a skew field K. An element x is called an involution if x2 = 1. In this paper, an involution is allowed to be the
【机 构】
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Department of Applied Mathematics,Department of Mathematics
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Consider the stable Steinberg group St(K) over a skew field K. An element x is called an involution if x2 = 1. In this paper, an involution is allowed to be the identity.The authors prove that an element A of GLn(K) up to conjugation can be represented as BC, where B is lower triangular and C is simultaneously upper triangular. Furthermore,B and C can be chosen so that the elements in the main diagonal of B are β1,β2,…,βn,and of C are γ1,γ2,…,γnCn,where cn ∈[K*,K*] and ∏n j=l-βjγj=det A.It is also proved that every element δ in St(K) is a product of 10 involutions.
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