Cofiniteness of local cohomology modules

Bigdelie, Mina and Zamani, Naser and Moghimi, Mohammad Bagher and Azami, Jafar (2010) Cofiniteness of local cohomology modules. Other thesis, University of Mohaghegh Ardabili.

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Abstract

Let R be a Noetherian ring and M be a non-zero finitely generated R-module. Let I be an ideal of R and t a non-negative integer. In this dissertation it is proved that for any minimax submodule N of HtI(M), the R-module HomR(R/I, HtI(M)/N) is finitely generated, whenever the modules H0I(M), H1I(M), ... , Ht-1I(M) are minimax. As a consequence, it follows that the associated primes of the R-module HtI(M)/N are finite. While dim SuppR HiI(M)≤1 for all i<t, It is shown that the R-modules H0I(M), H1I(M), … , Ht-1I(M) are cofinite and HomR(R/I, HtI(M)) is finitely generated. This implies that if dim R/I=1, then HiI(M) is I-cofinite for all i≥0. Also it is proved that if R is local and dim SuppR HiI(M)≤2 for all i<t, then the R-modules ExtRj(R/I, HiI(M)) and HomR(R/I, HtI(M)) are weakly Laskerian for all i<t and all j≥0. As a consequence, it follows that the set of associated primes of HiI(M) is finite for all i≥0, whenever dim R/I≤2.

Item Type: Thesis (Other)
Persian Title: هم¬متناهي بودن مدول¬هاي کوهمولوژي موضعي
Persian Abstract: فرض کنيم حلقه¬اي نوتري و يک ـ مدول غير صفر مولد¬متناهي باشد. همچنين فرض کنيم ايده¬آلي از و يک عدد صحيح نامنفي باشد. در اين پايان¬نامه ثابت مي¬شود هرگاه ـ مدول¬هاي , . . . , مينيماکس باشند آنگاه به ازاي هر زيرمدول مينيماکس نظير ، ـ مدول مولد¬متناهي بوده و در¬نتيجه مجموعه ايده¬آل¬هاي اول وابسته متناهي است. در حالتي که به ازاي هر ، 1 ، نشان داده مي¬شود که ـ مدول¬هاي , . . . , ، ـ هم¬متناهي هستند و مولد¬متناهي است. در¬نتيجه اگر ۱= ، آنگاه به ازاي هر 0 ، ـ هم¬متناهي است. همچنين ثابت مي¬شود که اگر حلقه¬اي موضعي باشد و به ازاي هر ، ، آنگاه به ازاي هر هر لاسکري ضعيف هستند. به عنوان يک نتيجه هرگاه ، آنگاه مجموعه ايده¬آل¬هاي اول وابسته به ازاي هر 0 متناهي است.
Supervisor:
SupervisorE-mail
Zamani, NaserUNSPECIFIED
Advisor:
AdvisorE-mail
Moghimi, Mohammad BagherUNSPECIFIED
Azami, JafarUNSPECIFIED
Subjects: Faculty of Basic Sciences > Department of Mathematics
Divisions > Faculty of Basic Sciences > Department of Mathematics
Divisions: Subjects > Faculty of Basic Sciences > Department of Mathematics
Faculty of Basic Sciences > Department of Mathematics
Date Deposited: 13 Jul 2019 09:30
Last Modified: 13 Jul 2019 09:30
URI: http://repository.uma.ac.ir/id/eprint/7873

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