This article is cited in 94 papers

Serre's problem on projective modules over polynomial rings, and algebraic $K$-theory

L. N. Vaserstein, A. A. Suslin


Abstract: We obtain new results on the freeness of projective modules over polynomial rings. In particular we prove the freeness of all projective modules over polynomial rings in five variables with coefficients from an arbitrary field.
Bibliography: 46 titles.

UDC: 519.4

MSC: Primary 13C10, 13F20, 14F05; Secondary 13B25, 18F25

Received: 04.04.1975

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:5, 937–1001

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