TY - JOUR
T1 - J-Multiplicity and depth of associated graded modules
AU - Polini, Claudia
AU - Xie, Yu
N1 - Funding Information:
E-mail addresses: [email protected] (C. Polini), [email protected] (Y. Xie). 1 The author was partially supported by the NSF and the NSA.
PY - 2013/4/1
Y1 - 2013/4/1
N2 - Let R be a Noetherian local ring. We define the minimal j-multiplicity and almost minimal j-multiplicity of an arbitrary R-ideal on any finite R-module. For any ideal I with minimal j-multiplicity or almost minimal j-multiplicity on a Cohen-Macaulay module M, we prove that under some residual conditions, the associated graded module grI(M) is Cohen-Macaulay or almost Cohen-Macaulay, respectively. Our work generalizes the results for minimal multiplicity and almost minimal multiplicity obtained by Sally, Rossi, Valla, Wang, Huckaba, Elias, Corso, Polini, and Vaz Pinto.
AB - Let R be a Noetherian local ring. We define the minimal j-multiplicity and almost minimal j-multiplicity of an arbitrary R-ideal on any finite R-module. For any ideal I with minimal j-multiplicity or almost minimal j-multiplicity on a Cohen-Macaulay module M, we prove that under some residual conditions, the associated graded module grI(M) is Cohen-Macaulay or almost Cohen-Macaulay, respectively. Our work generalizes the results for minimal multiplicity and almost minimal multiplicity obtained by Sally, Rossi, Valla, Wang, Huckaba, Elias, Corso, Polini, and Vaz Pinto.
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U2 - 10.1016/j.jalgebra.2013.01.001
DO - 10.1016/j.jalgebra.2013.01.001
M3 - Article
AN - SCOPUS:84872827169
SN - 0021-8693
VL - 379
SP - 31
EP - 49
JO - Journal of Algebra
JF - Journal of Algebra
ER -