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- W1980974501 abstract "A well-known lemma of Suslin says that for a commutative ring A if ( v 1 ( X ) , … , v n ( X ) ) ∈ ( A [ X ] ) n is unimodular where v 1 is monic and n ≥ 3 , then there exist γ 1 , … , γ ℓ ∈ E n − 1 ( A [ X ] ) such that the ideal generated by Res ( v 1 , e 1 . γ 1 t ( v 2 , … , v n ) ) , … , Res ( v 1 , e 1 . γ ℓ t ( v 2 , … , v n ) ) equals A . This lemma played a central role in the resolution of Serre’s Conjecture. In the case where A contains a set E of cardinality greater than deg v 1 + 1 such that y − y ′ is invertible for each y ≠ y ′ in E , we prove that the γ i can simply correspond to the elementary operations L 1 → L 1 + y i ∑ j = 2 n − 1 u j + 1 L j , 1 ≤ i ≤ ℓ = deg v 1 + 1 , where u 1 v 1 + ⋯ + u n v n = 1 . These efficient elementary operations enable us to give new and simple algorithms for reducing unimodular rows with entries in K [ X 1 , … , X k ] to t ( 1 , 0 , … , 0 ) using elementary operations in the case where K is an infinite field. Another feature of this paper is that it shows that the concrete local–global principles can produce competitive complexity bounds." @default.
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- W1980974501 date "2005-06-01" @default.
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- W1980974501 title "Suslin’s algorithms for reduction of unimodular rows" @default.
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- W1980974501 doi "https://doi.org/10.1016/j.jsc.2005.01.004" @default.
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