Reciprocity laws and the stable rank of polynomial rings

A. A. Suslin

doi:10.1070/IM1980v015n03ABEH001270

Reciprocity laws and the stable rank of polynomial rings

A. A. Suslin

Mathematics

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9 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,…, X_n] 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 language	English (US)
Pages (from-to)	589-623
Number of pages	35
Journal	Mathematics of the USSR - Izvestija
Volume	15
Issue number	3
DOIs	https://doi.org/10.1070/IM1980v015n03ABEH001270
State	Published - Jun 30 1980

ASJC Scopus subject areas

Mathematics(all)

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10.1070/IM1980v015n03ABEH001270

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title = "Reciprocity laws and the stable rank of polynomial rings",

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.",

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AB - 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.

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JO - Mathematics of the USSR - Izvestija

JF - Mathematics of the USSR - Izvestija

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ER -

Reciprocity laws and the stable rank of polynomial rings

Abstract

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