کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4597765 | 1336231 | 2008 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Graphs and the Jacobian conjecture
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
It is proved in [M. de Bondt, A. van den Essen, A reduction of the Jacobian conjecture to the symmetric case, Proceedings of the AMS 133 (8) (2005) 2201-2205] that it suffices to study the Jacobian Conjecture for maps of the form x+âf, where f is a homogeneous polynomial of degree d(=4). The Jacobian Condition implies that f is a finite sum of d-th powers of linear forms, ãα,xãd, where ãx,yã=xty and each α is an isotropic vector i.e. ãα,αã=0. To a set {α1,â¦,αs} of isotropic vectors, we assign a graph and study its structure in case the corresponding polynomial f=âãαj,xãd has a nilpotent Hessian. The main result of this article asserts that in the case dim([α1,â¦,αs])â¤2 or â¥sâ2, the Jacobian Conjecture holds for the maps x+âf. In fact, we give a complete description of the graphs of such f's, whose Hessian is nilpotent. As an application of the result, we show that lines and cycles cannot appear as graphs of HN polynomials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 212, Issue 3, March 2008, Pages 578-598
Journal: Journal of Pure and Applied Algebra - Volume 212, Issue 3, March 2008, Pages 578-598
نویسندگان
Arno van den Essen, Roel Willems,