Mixed multiplicities and the minimal number of generator of modules |
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Authors: | R Callejas-Bedregal VH Jorge Pérez |
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Institution: | a Universidade Federal da Paraíba-DM, 58.051-900, João Pessoa, PB, Brazil b Universidade de São Paulo - ICMC, Caixa Postal 668, 13560-970, São Carlos-SP, Brazil |
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Abstract: | Let (R,m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of Rp of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees’ mixed multiplicity theorem, which was first proved by Kirby and Rees in (1994, 8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of Rp in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, 5]) for m-primary ideals. |
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Keywords: | Primary 13H15 |
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