A note on the coefficients of Hilbert characteristic functions in semi-regular local rings
1963 ◽
Vol 59
(2)
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pp. 269-275
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Keyword(s):
Let Q be a semi-regular local ring of dimension d, m be its maximal ideal, and q be an m-primary ideal. Then LQ(Q/qn+1), the length of Q-module Q/qn+1, is equal to the characteristic polynomial PQ(q,n) in n for a sufficiently large value of n:where ei = ei(q), i = 0,1,2,…, d are integers uniquely determined by q, called normalized Hilbert coefficients of q according to (1). It was shown in (1) that e1(q) is a non-negative integer, and is equal to zero if and only if q is generated by a system of parameters. We shall prove, in this paper, that e2(q) is also a non-negative integer, and that this non-negativity is not necessarily true for other coefficients. We shall give an example with negative e3(q).
2010 ◽
Vol 199
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pp. 95-105
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1954 ◽
Vol 50
(2)
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pp. 145-158
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Keyword(s):
1985 ◽
Vol 28
(3)
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pp. 349-353
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Keyword(s):
1994 ◽
Vol 136
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pp. 133-155
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2010 ◽
Vol 199
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pp. 95-105
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Keyword(s):
1996 ◽
Vol 120
(1)
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pp. 31-42
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Keyword(s):
2019 ◽
Vol 19
(04)
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pp. 2050061
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1992 ◽
Vol 111
(1)
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pp. 47-56
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Keyword(s):
2016 ◽
Vol 16
(09)
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pp. 1750163
Keyword(s):
2021 ◽
pp. 49-62
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