Gorenstein injective dimension and a generalization of Ischebeck Formula

Reza Sazeedeh

Gorenstein injective dimension and a generalization of Ischebeck Formula

Commutative Algebra 2011-05-13 v1

Authors: Reza Sazeedeh

Abstract

Let $(R,\frak m)$ be a commutative Noetherian local ring and let $M$ and $N$ be finitely generated $R$ -modules of finite injective dimension and finite Gorenstein injective dimension, respectively. In this paper we prove a generalization of Ischebeck Formula, that is $\depth_RM+\sup\{i| {0.1cm}\Ext_R^i(M,N)\neq 0\}=\depth R.$

Keywords

Gorenstein injective dimension Ischebeck Formula commutative Noetherian local ring depth Ext functor finitely generated module injective dimension

Cite

@article{arxiv.1105.2399,
  title  = {Gorenstein injective dimension and a generalization of Ischebeck Formula},
  author = {Reza Sazeedeh},
  journal= {arXiv preprint arXiv:1105.2399},
  year   = {2011}
}

Comments

5 pages

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