کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4597901 1336237 2006 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stanley–Reisner rings and the radicals of lattice ideals
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Stanley–Reisner rings and the radicals of lattice ideals
چکیده انگلیسی

In this article we associate to every lattice ideal IL,ρ⊂K[x1,…,xm]IL,ρ⊂K[x1,…,xm] a cone σσ and a simplicial complex ΔσΔσ with vertices the minimal generators of the Stanley–Reisner ideal of σσ. We assign a simplicial subcomplex Δσ(F)Δσ(F) of ΔσΔσ to every polynomial F  . If F1,…,FsF1,…,Fs generate IL,ρIL,ρ or they generate rad(IL,ρ)rad(IL,ρ) up to radical, then ⋃i=1sΔσ(Fi) is a spanning subcomplex of ΔσΔσ. This result provides a lower bound for the minimal number of generators of IL,ρIL,ρ which improves the generalized Krull's principal ideal theorem for lattice ideals. But mainly it provides lower bounds for the binomial arithmetical rank and the A-homogeneous arithmetical rank of a lattice ideal. Finally, we show by a family of examples that the given bounds are sharp.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 204, Issue 3, March 2006, Pages 584–601
نویسندگان
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