  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.
