Youla, D. C.; Pickel, P. F. The Quillen-Suslin theorem and the structure of \(n\)-dimensional elementary polynomial matrices. (English) Zbl 0553.13003 IEEE Trans. Circuits Syst. 31, 513-518 (1984). 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 Cited in 37 Documents MSC: 13C10 Projective and free modules and ideals in commutative rings Keywords:Serre conjecture; freeness of finitely generated projective modules; Quillen-Suslin theorem Citations:Zbl 0373.13004 PDFBibTeX XMLCite \textit{D. C. Youla} and \textit{P. F. Pickel}, IEEE Trans. Circuits Syst. 31, 513--518 (1984; Zbl 0553.13003) Full Text: DOI