When is there a nontrivial extension-closed subcategory?
Commutative Algebra
2011-01-06 v1 Representation Theory
Abstract
Let R be a commutative Noetherian local ring, and denote by mod R the category of finitely generated R-modules. In this paper, we consider when mod R has a nontrivial extension-closed subcategory. We prove that this is the case if there are part of a minimal system of generators x,y of the maximal ideal with xy=0, and that it holds if R is a stretched Artinian Gorenstein local ring which is not a hypersurface.
Cite
@article{arxiv.1101.0991,
title = {When is there a nontrivial extension-closed subcategory?},
author = {Ryo Takahashi},
journal= {arXiv preprint arXiv:1101.0991},
year = {2011}
}
Comments
12 pages, to appear in Journal of Algebra