کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4584628 | 1630495 | 2014 | 14 صفحه PDF | دانلود رایگان |
We study, by means of embeddings of Hilbert functions, a class of rings which we call Shakin rings, i.e. quotients K[X1,…,Xn]/aK[X1,…,Xn]/a of a polynomial ring over a field K by ideals a=L+Pa=L+P which are the sum of a piecewise lex-segment ideal L, as defined by Shakin, and a pure powers ideal P . Our main results extend Abedelfatah's recent work on the Eisenbud–Green–Harris Conjecture, Shakin's generalization of Macaulay and Bigatti–Hulett–Pardue Theorems on Betti numbers and, when char(K)=0char(K)=0, Mermin–Murai Theorem on the Lex-Plus-Power inequality, from monomial regular sequences to a larger class of ideals. We also prove an extremality property of embeddings induced by distractions in terms of Hilbert functions of local cohomology modules.
Journal: Journal of Algebra - Volume 419, 1 December 2014, Pages 318–331