A polynomial bound on the number of comaximal localizations needed in order to make free a projective module |
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Authors: | Gema M. Diaz-Toca Henri Lombardi |
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Affiliation: | a Dpto. de Matemática Aplicada, Universidad de Murcia, Spain b Équipe de Mathématiques, UMR CNRS 6623, Université de Franche-Comté, France |
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Abstract: | Let A be a commutative ring and M be a projective module of rank k with n generators. Let h=n-k. Standard computations show that M becomes free after localizations in comaximal elements (see Theorem 5). When the base ring A contains a field with at least hk+1 non-zero distinct elements we construct a comaximal family G with at most (hk+1)(nk+1) elements such that for each g∈G, the module Mg is free over A[1/g]. |
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