Maximal ideals in module categories and applications

2017/10/19 by Cortés-Izurdiaga, Manuel, Facchini, Alberto
#16D90 #16P40 #18E05 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1710.07053

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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