Reciprocity laws and the stable rank of polynomial rings

A. A. Suslin

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Reciprocity laws and Mennicke symbols for regular rings of arbitrary dimension are introduced and studied. The universal Mennicke symbol for the polynomial ring k[X1,…, Xn] relative to the principal ideal (Equation presented) 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.

Original languageEnglish (US)
Pages (from-to)589-623
Number of pages35
JournalMathematics of the USSR - Izvestija
Volume15
Issue number3
DOIs
StatePublished - Jun 30 1980

ASJC Scopus subject areas

  • Mathematics(all)

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