Mixed multiplicities and the minimal number of generator of modules

Autor(es)

Callejas-Bedregal, R. ^[1] ; Jorge Perez, V. H. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Paraiba, DM, BR-58051900 Joao Pessoa, Paraiba - Brazil

^[2] Univ Sao Paulo, ICMC, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Pure and Applied Algebra; v. 214, n. 9, p. 1642-1653, SEP 2010.
• Citações Web of Science: 7

Resumo

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 R(p) 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 R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, {[}5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 08/53703-0 - Roberto Callejas Bedregal | Universidade Federal daParaíba /UFPB - Brasil
• Beneficiário: Victor Hugo Jorge Pérez
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil