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Computation of $K\sb 1$ via Mennicke symbols. (English) Zbl 0614.16018
Let R be a ring. The author filters $K\sb 1R$ by the Whitehead determinants of invertible matrices over R and computes the corresponding graded group in terms of symbols which generalize Mennicke’s symbol. In addition, the result of {\it H. Bass}, {\it J. Milnor} and {\it J.-P. Serre} [Publ. Math., Inst. Hautes Etud. Sci. 33, 59-137 (1967; Zbl 0174.052)] on SK${}\sb 1$R of a Dedekind ring R is generalized via the Mennicke symbol to an arbitrary commutative ring R satisfying the Bass second stable range condition.
Reviewer: M.Golasiński

16E20Grothendieck groups and $K$-theory of noncommutative rings
13D15$K$-theory (commutative rings)
18F25Algebraic $K$-theory and $L$-theory
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