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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An elementary transformation of a special unimodular vector to its top coefficient vector


Author: Ravi A. Rao
Journal: Proc. Amer. Math. Soc. 93 (1985), 21-24
MSC: Primary 13D15; Secondary 13B25
DOI: https://doi.org/10.1090/S0002-9939-1985-0766519-0
MathSciNet review: 766519
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Abstract: Let $ R$ be a commutative ring, $ {\mathbf{v}}(X)$ a unimodular $ n$-vector $ (n \geqslant 3)$ over $ R[X]$. Suppose the leading coefficients in $ {\mathbf{v}}(X)$ form a unimodular vector $ L({\mathbf{v}})$ over $ R$. Then some element in $ {E_n}(R[X])$ will transform $ {\mathbf{v}}(X)$ to $ L({\mathbf{v}})$.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0766519-0
Article copyright: © Copyright 1985 American Mathematical Society