کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771704 | 1630426 | 2017 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Finitely supported â-simple complete ideals and multiplicities in a regular local ring
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Finitely supported â-simple complete ideals and multiplicities in a regular local ring Finitely supported â-simple complete ideals and multiplicities in a regular local ring](/preview/png/5771704.png)
چکیده انگلیسی
Let (R,m) and (S,n) be regular local rings of dimâ¡(S)=dimâ¡(R)â¥2 such that S birationally dominates R, and let V be the order valuation ring of S with corresponding valuation ν:=ordS. Assume that ISâ S and νâReesSIS. Let u:=αt with IS=αIS, where αâS. Then V=Wâ©Q(R) with W=(R[It]â¾)Q=(S[ISu]â¾)Qâ², where QâMin(mR[It]â¾) and Qâ²âMin(nS[ISu]â¾). Let P,Pâ² be the center of W on R[It] and S[Isu], respectively. We prove that if [Sn:Rm]=1, then R[It]P=S[Isu]Pâ². Let I be a finitely supported complete m-primary ideal of a regular local ring (R,m) of dimension dâ¥2. Let T be a terminal base point of I and V be the mT-adic order valuation of T with corresponding valuation v:=ordT. Let nâ¥1 be an integer. Assume that IT=mTn and [TmT:Rm]=1. Let PâMin(mR[It]) such that P=Qâ©R[It] with V=(R[It]â¾)Qâ©Q(R), where QâMin(mR[It]â¾). We prove that the quotient ring R[It]P is d-dimensional normal Cohen-Macaulay standard graded domain over k with the multiplicity ndâ1. In particular, R[It]P is regular if and only if n=1. We prove that k:=Rm is relatively algebraically closed in kv:=VmV. Also we determine the multiplicity of R[It]P, and we prove that if IT=mT, then R[It]P is regular if and only if [TmT:Rm]=1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 488, 15 October 2017, Pages 290-314
Journal: Journal of Algebra - Volume 488, 15 October 2017, Pages 290-314
نویسندگان
Mee-Kyoung Kim,