Mohan Kumar, N. A note on unimodular rows. (English) Zbl 0901.13009 J. Algebra 191, No. 1, 228-234 (1997). The aim of the paper is to show the following: Let \(k\) be an algebraically closed field and let \(R=k [X_0, \dots, X_n]\). Suppose we are given the unimodular row \((f_0, \dots, f_n)\) with homogeneous polynomials. Assume \(n!\mid \ell(R/(f_0, \dots, f_n))\), where \(\ell\) means length. Then the unimodular row \((f_0, \dots, f_n)\) is completable, i.e. there is \(A\in\text{GL}(n+1,R)\) such that \(A(f_0, \dots, f_n)= (1,0, \dots,0)\). This gives an answer in a special case to a question of Nori about unimodular rows, a question generalizing a theorem of Suslin. Reviewer: Christodor Ionescu (Bucureşti) Cited in 1 ReviewCited in 3 Documents MSC: 13C10 Projective and free modules and ideals in commutative rings 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 19A13 Stability for projective modules Keywords:unimodular row; homogeneous polynomials; length PDFBibTeX XMLCite \textit{N. Mohan Kumar}, J. Algebra 191, No. 1, 228--234 (1997; Zbl 0901.13009) Full Text: DOI References: [1] Mumford, D., Algebraic Geometry I, Complex Projective Varieties, Grundlehren der mathematischen Wissenschaften (1976), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0356.14002 [2] Quillen, D., Projective modules over polynomial rings, Invent. Math., 36, 166-172 (1976) [3] Suslin, A. A., Stably free modules, Mat. Sb., 102, 537-550 (1977) · Zbl 0389.13002 [4] Swan, R. G., Vector bundles, projective modules and the \(K\), John Moore Conference. John Moore Conference, Annals of Mathematics Studies, 113 (1987), Princeton Univ. Press: Princeton Univ. Press Princeton, p. 432-522 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.