تقرير
On the Rees algebra and the conductor of an ideal
| العنوان: | On the Rees algebra and the conductor of an ideal |
|---|---|
| المؤلفون: | Gasanova, Oleksandra, Herzog, Jürgen, Kling, Filip Jonsson, Moradi, Somayeh |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, 13A30 (Primary) 05E40 (Secondary) |
| الوصف: | For an ideal $I$ in a Noetherian ring $R$, we introduce and study its conductor as a tool to explore the Rees algebra of $I$. The conductor of $I$ is an ideal $C(I)\subset R$ obtained from the defining ideals of the Rees algebra and the symmetric algebra of $I$ by a colon operation. Using this concept we investigate when adding an element to an ideal preserves the property of being of linear type. In this regard, a generalization of a result by Valla in terms of the conductor ideal is presented. When the conductor of a graded ideal in a polynomial ring is the graded maximal ideal, a criteria is given for when the Rees algebra and the symmetric algebra have the same Krull dimension. Finally, noting the fact that the conductor of a monomial ideal is a monomial ideal, the conductor of some families of monomial ideals, namely bounded Veronese ideals and edge ideals of graphs, are determined. Comment: 16 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06922 |
| رقم الأكسشن: | edsarx.2407.06922 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |