MULTIPLICITIES FOR ARBITRARY MODULES AND REDUCTION

作者：Callejas Bedregal R^*; Jorge Perez V H

来源：Rocky Mountain Journal of Mathematics, 2013, 43(4): 1077-1113.

DOI：10.1216/RMJ-2013-43-4-1077

• Integral closure
• multiplicity sequence

Let (R, m) be a d-dimensional Noetherian local ring and E a finitely generated R-submodule of the free module R-p. In this work, we introduce a multiplicity sequence c(k)(E), k = 0, ... , d + p - 1, for E that generalizes the Buchsbaum-Rim multiplicity defined when E has finite colength in R-p as well as the Achilles-Manaresi multiplicity sequence that applies when E subset of R is an ideal. Our main results are that the new multiplicity sequence is an invariant of E up to reduction; we show that this multiplicity sequence behaves well with respect to sufficiently general hyperplane sections, and we also give a criterion for reduction of ideals involving the c(0)-multiplicity in all localizations in prime ideals.

• 出版日期2013