Article
Constructions in R[x_1, ..., x_n]. Applications to K-Theory
Author/s | Gago Vargas, Manuel Jesús |
Department | Universidad de Sevilla. Departamento de Álgebra |
Publication Date | 2002-06-25 |
Deposit Date | 2015-03-25 |
Published in |
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Abstract | A classical result in K-Theory about polynomial rings like the Quillen-Suslin
theorem admits an algorithmic approach when the ring of coefficients has some
computational properties, associated with Gröbner bases. There ... A classical result in K-Theory about polynomial rings like the Quillen-Suslin theorem admits an algorithmic approach when the ring of coefficients has some computational properties, associated with Gröbner bases. There are several algorithms when we work in $\K[\x]$, $\K$ a field. In this paper we compute a free basis of a finitely generated projective module over $R[\x]$, $R$ a principal ideal domain with additional properties, test the freeness for projective modules over $D[\x]$, with $D$ a Dedekind domain like $\Zset[\sqrt{-5}]$ and for the one variable case compute a free basis if there exists any. |
Funding agencies | Junta de Andalucía |
Citation | Gago Vargas, M.J. (2002). Constructions in R[x_1, ..., x_n]. Applications to K-Theory. Journal of Pure and Applied Algebra, 171 (2-3), 185-196. |
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