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arXiv · 1508.07518

Graded-irreducible modules are irreducible

Justin Chen·Youngsu Kim
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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.

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Justin Chen, Youngsu Kim. 2016-09-29. Graded-irreducible modules are irreducible. https://arxiv.org/abs/1508.07518

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