کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9497168 | 1630754 | 2005 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The Gorenstein and complete intersection properties of associated graded rings
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The Gorenstein and complete intersection properties of associated graded rings The Gorenstein and complete intersection properties of associated graded rings](/preview/png/9497168.png)
چکیده انگلیسی
Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F(I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free over R/I, we observe that: (i) G(I) is Cohen-Macaulay iff F(I) is Cohen-Macaulay, (ii) G(I) is Gorenstein iff both F(I) and R/I are Gorenstein, and (iii) G(I) is a relative complete intersection iff F(I) is a complete intersection. In case (R,m) is Gorenstein, we give a necessary and sufficient condition for G(I) to be Gorenstein in terms of residuation of powers of I with respect to a reduction J of I with μ(J)=dimR and the reduction number r of I with respect to J. We prove that G(I) is Gorenstein if and only if J:Ir-i=J+Ii+1 for 0⩽i⩽r-1. If (R,m) is a Gorenstein local ring and Iâm is an ideal having a reduction J with reduction number r such that μ(J)=ht(I)=g>0, we prove that the extended Rees algebra R[It,t-1] is quasi-Gorenstein with a-invariant a if and only if Ji:Ir=Ii+a-r+g-1 for every iâZ. If, in addition, dimR=1, we show that G(I) is Gorenstein if and only if Ji:Ir=Ii for 1⩽i⩽r.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 201, Issues 1â3, 1 October 2005, Pages 264-283
Journal: Journal of Pure and Applied Algebra - Volume 201, Issues 1â3, 1 October 2005, Pages 264-283
نویسندگان
William Heinzer, Mee-Kyoung Kim, Bernd Ulrich,