ON A NEW INVARIANT OF FINITELY GENERATED MODULES OVER LOCAL RINGS
2010 ◽
Vol 09
(06)
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pp. 959-976
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Let M be a finitely generated module on a local ring R and [Formula: see text] a filtration of submodules of M such that do < d1 < ⋯ < dt = d, where di = dim Mi. This paper is concerned with a non-negative integer [Formula: see text] which is defined as the least degree of all polynomials in n1, …, nd bounding above the function [Formula: see text] We prove that [Formula: see text] is independent of the choice of good systems of parameters [Formula: see text]. When [Formula: see text] is the dimension filtration of M, we can use the polynomial type of Mi/Mi-1 and the dimension of the non-sequentially Cohen–Macaulay locus of M to compute [Formula: see text], and also to study the behavior of it under local flat homomorphisms.
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2018 ◽
Vol 17
(11)
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pp. 1850202
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2016 ◽
Vol 16
(09)
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pp. 1750163
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1992 ◽
Vol 111
(1)
◽
pp. 25-33
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