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The Quillen-Suslin theorem and the structure of \(n\)-dimensional elementary polynomial matrices. (English) Zbl 0553.13003

The authors present a tutorial introduction to the Quillen-Suslin theorem (”Serre’s conjecture”), that finitely generated projective R-modules are free, for R a polynomial ring over a field. The proof, a variation of that found in Lam’s book [cf. T. Y. Lam, ”Serre’s conjecture”, Lect. Notes Math. 635 (1978; Zbl 0373.13004)], is given with a minimum of algebraic terminology. Basically only easy polynomial algebra is assumed from the reader.
Reviewer: E.Sontag

MSC:

13C10 Projective and free modules and ideals in commutative rings

Citations:

Zbl 0373.13004
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