کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4584893 | 1630513 | 2014 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Finitely supported â-simple complete ideals in a regular local ring
ترجمه فارسی عنوان
آکا کاملترین پشتیبانی شده است؟ - ایده آل کامل ساده در یک حلقه محلی به طور منظم
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let I be a finitely supported complete m-primary ideal of a regular local ring (R,m). A theorem of Lipman implies that I has a unique factorization as a â-product of special â-simple complete ideals with possibly negative exponents for some of the factors. The existence of negative exponents occurs if dimR⩾3 because of the existence of finitely supported â-simple ideals that are not special. We consider properties of special â-simple complete ideals such as their Rees valuations and point basis. Let (R,m) be a d-dimensional equicharacteristic regular local ring with m=(x1,â¦,xd)R. We define monomial quadratic transforms of R and consider transforms and inverse transforms of monomial ideals. For a large class of monomial ideals I that includes complete inverse transforms, we prove that the minimal number of generators of I is completely determined by the order of I. We give necessary and sufficient conditions for the complete inverse transform of a â-product of monomial ideals to be the â-product of the complete inverse transforms of the factors. This yields examples of finitely supported â-simple monomial ideals that are not special. We prove that a finitely supported â-simple monomial ideal with linearly ordered base points is special â-simple.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 401, 1 March 2014, Pages 76-106
Journal: Journal of Algebra - Volume 401, 1 March 2014, Pages 76-106
نویسندگان
William Heinzer, Mee-Kyoung Kim, Matthew Toeniskoetter,