A Presentation for the Unipotent Group over Rings with Identity
نویسندگان
چکیده
Ž . For a ring R with identity, define Unip R to be the group of upper-triangular n matrices over R all of whose diagonal entries are 1. For i 1, 2, . . . , n 1, let Si denote the matrix whose only nonzero off-diagonal entry is a 1 in the ith row and Ž . Ž . i 1 st column. Then for any integer m including m 0 , it is easy to see that Ž . the S generate Unip Z mZ . Reiner gave relations among the S which he i n i Ž . conjectured gave a presentation for Unip Z 2Z . This conjecture was proven by n Ž . Biss Comm. Algebra 26 1998 , 2971 2975 and an analogous conjecture was made Ž . for Unip Z mZ in general. We prove this conjecture, as well as a generalization n of the conjecture to unipotent groups over arbitrary rings. 2001 Academic Press
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