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arXiv · 1710.07053

Maximal ideals in module categories and applications

Manuel Cortés-Izurdiaga·Alberto Facchini
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Abstract

We study the existence of maximal ideals in preadditive categories defining an order $\preceq$ between objects, in such a way that if there do not exist maximal objects with respect to $\preceq$, then there is no maximal ideal in the category. In our study, it is sometimes sufficient to restrict our attention to suitable subcategories. We give an example of a category $\mathbf C_F$ of modules over a right noetherian ring $R$ in which there is a unique maximal ideal. The category $\mathbf C_F$ is related to an indecomposable injective module $F$, and the objects of $\mathbf C_F$ are the $R$-modules of finite $F$-rank.

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Manuel Cortés-Izurdiaga, Alberto Facchini. 2017-10-19. Maximal ideals in module categories and applications. https://arxiv.org/abs/1710.07053

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