Completion of skew completable unimodular rows

Sampat Sharma ()
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Sampat Sharma: Indian Institute of Technology Bombay

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 1, 181-187

Abstract: Abstract In this paper, we prove that if R is a local ring of dimension $$d\ge 3$$ d ≥ 3 , d odd and $$\frac{1}{(d-1)!}\in R$$ 1 ( d - 1 ) ! ∈ R then any skew completable unimodular row $$v\in Um_{d}(R[X])$$ v ∈ U m d ( R [ X ] ) is completable. It is also proved that skew completable unimodular rows of size $$d\ge 3$$ d ≥ 3 over a regular local ring of dimension d are first row of a 2- stably elementary matrix.

Keywords: Local ring; Regular local ring; Witt group; 13C10; 13H99; 19B10; 19B14 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00090-z

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