Graded-irreducible modules are irreducible
Commutative Algebra
2016-10-03 v2
Abstract
We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural extension of the index of reducibility to the graded setting coincides with the ordinary index of reducibility. We also investigate the question of uniqueness of the components in a graded-irreducible decomposition, as well as the relation between the index of reducibility of a non-graded ideal and that of its largest graded subideal.
Cite
@article{arxiv.1508.07518,
title = {Graded-irreducible modules are irreducible},
author = {Justin Chen and Youngsu Kim},
journal= {arXiv preprint arXiv:1508.07518},
year = {2016}
}
Comments
Comments are welcome, to appear in Communications in Algebra