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A note on Castelnuovo-Mumford regularity and Hilbert coefficients. (English) Zbl 1423.13094

##### MSC:
 13D45 Local cohomology and commutative rings 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
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##### References:
 [1] Blancafort, C., Hilbert functions of graded algebras over Artinian rings, J. Pure Appl. Algebra, 125, 55-78, (1998) · Zbl 0893.13004 [2] Brodmann, M. P.; Sharp, R. Y., Local Cohomology: An Algebraic Introduction with Geometric Applications, 136, (2013), Cambridge University Press: Cambridge University Press, Cambridge · Zbl 0903.13006 [3] Bruns, W.; Herzog, J., Cohen-Macaulay Rings, 39, (1993), Cambridge University Press: Cambridge University Press, Cambridge [4] Chardin, M.; Moreno-Socias, G., Regularity of lex-segment ideals: Some closed formulas and applications, Proc. Amer. Math. Soc., 131, 1093-1102, (2003) · Zbl 1036.13014 [5] L. X. Dung and L. T. Hoa, Dependence of Hilbert coefficients, Manuscripta Math.149 (2016) 235-249, Erratum 154 (2017) 551-552. [6] Hoa, L. T., Reduction numbers of equimultiple ideals, J. Pure Appl. Algebra, 109, 111-126, (1996) · Zbl 0877.13002 [7] Hoa, L. T.; Hyry, E., Castelnuovo-Mumford regularity of initial ideals, J. Symb. Comp., 38, 1327-1341, (2004) · Zbl 1137.13307 [8] Kirby, D.; Mehran, H. A., A note on the coefficients of the Hilbert-Samuel polynomial for a Cohen-Macaulay module, J. London Math. Soc., 25, 2, 449-457, (1982) · Zbl 0455.13005 [9] Rossi, M. E.; Trung, N. V.; Valla, G., Castelnuovo-Mumford regularity and extended degree, Trans. Amer. Math. Soc., 355, 1773-1786, (2003) · Zbl 1075.13008 [10] Srinivas, V.; Trivedi, V., On the Hilbert function of a Cohen-Macaulay local ring, J. Algebraic Geom., 6, 733-751, (1997) · Zbl 0957.13009 [11] Trivedi, V., Hilbert functions, Castelnuovo-Mumford regularity and uniform Artin-Rees numbers, Manuscripta Math., 94, 485-499, (1997) · Zbl 0893.13003
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