Cominimaxness of certain general local cohomology modules

Moharram AGHAPOURNAHR

Makale detayları

Cominimaxness of certain general local cohomology modules

Yazarlar:

Moharram AGHAPOURNAHR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 4, pp.1121-1130

Belge Tipi:

Makale

Yayın Tarihi:

8/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000451483

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

Özet:

 

Let RRR be a commutative Noetherian ring, ΦΦ\Phi a system of ideals of RRR and I∈ΦI∈ΦI\in \Phi. Let t∈N0t∈N0t\in\Bbb{N}_0 be an integer and MMM an RRR-module such that ExtiR(R/I,M)ExtRi(R/I,M)Ext^i_R(R/I,M) is minimax for all i≤t+1i≤t+1i\leq t+1. We prove that if the RRR-module HiΦ(M)HΦi(M)H^{i}_\Phi(M) is FD≤1FD≤1{FD_{\leq 1}} (or weakly Laskerian) for all i<ti<ti<t, then HiΦ(M)HΦi(M)H^i_{\Phi}(M) is ΦΦ\Phi-cominimax for all i<ti<ti<t and for any FD≤0FD≤0FD_{\leq 0} (or minimax) submodule NNN of HtΦ(M)HΦt(M)H^t_{\Phi}(M), the RRR-modules HomR(R/I,HtΦ(M)/N)HomR(R/I,HΦt(M)/N)Hom_{R}(R/I,H^t_{\Phi}(M)/N) and Ext1R(R/I,HtΦ(M)/N)ExtR1(R/I,HΦt(M)/N)Ext^1_{R}(R/I,H^t_{\Phi}(M)/N) are minimax. Let NNN be a finitely generated RRR-module. We also prove that ExtjR(N,HiΦ(M))ExtRj(N,HΦi(M))Ext^j_{R}(N,H^i_\Phi(M)) and TorRj(N,HiΦ(M))TorjR(N,HΦi(M))Tor^R_{j}(N,H^i_{\Phi}(M)) are ΦΦ\Phi-cominimax for all iii and jjj whenever MMM is minimax and HiΦ(M)HΦi(M)H^i_{\Phi}(M) is FD≤1FD≤1{FD_{\leq 1}} (or weakly Laskerian) for all iii.

Makale detayları

Cominimaxness of certain general local cohomology modules

Yazarlar: Moharram AGHAPOURNAHR

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 4, pp.1121-1130

Belge Tipi: Makale

Yayın Tarihi: 8/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000451483

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

Moharram AGHAPOURNAHR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 4, pp.1121-1130

Belge Tipi:

Makale

Yayın Tarihi:

8/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000451483

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X