Abstract
Let M be a sequentially generalized Cohen–Macaulay module over a Noetherian local ring R and \(\mathcal {F}\) a generalized Cohen–Macaulay filtration of M. In this paper, we establish uniform bounds for the Castelnouvo–Mumford regularity of associated graded modules \(\text {reg}(G_{\mathfrak {q}}(M))\) and for the relation type \(\text {reltype}(\mathfrak {q})\) associated to all distinguished parameter ideals \(\mathfrak {q}\) with respect to \(\mathcal {F}\).
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Acknowledgments
The authors would like to thank the referee for her/his useful suggestions. This paper was finished during the authors’ visit at the Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi, Vietnam. They would like to thank VIASM for their support and hospitality.
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Dedicated to Professor Nguyen Khoa Son on the occasion of his 65 birthday.
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant numbers 101.04-2014.25 and 101.04-2014.15.
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Cuong, N.T., Long, N.T. & Truong, H.L. Uniform Bounds in Sequentially Generalized Cohen–Macaulay Modules. Vietnam J. Math. 43, 343–356 (2015). https://doi.org/10.1007/s10013-015-0126-2
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DOI: https://doi.org/10.1007/s10013-015-0126-2
Keywords
- Relation type
- Castelnouvo–Mumford regularity
- Sequentially generalized
- Cohen–Macaulay
- Generalized Cohen–Macaulay filtration
- Distinguished system of parameters