RECIPROCITY LAWS AND THE STABLE RANK OF POLYNOMIAL RINGS
Andrei A. Suslin · Mathematics of the USSR-Izvestiya · 1980
Reciprocity laws and Mennicke symbols for regular rings of arbitrary dimension are introduced and studied. The universal Mennicke symbol for the polynomial ring relative to the principal ideal is computed. The results obtained in this paper are applied to the problem of determining the precise value of the stable rank of polynomial rings and affine algebras over fields. Bibliography: 19 titles.