2 research outputs found
Maximal ideals in module categories and applications
We study the existence of maximal ideals in preadditive categories defining
an order between objects, in such a way that if there do not exist
maximal objects with respect to , 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 of modules over a right noetherian ring in which there is a unique
maximal ideal. The category is related to an indecomposable
injective module , and the objects of are the -modules of
finite -rank.Comment: Accepted for publication in Applied Categorical Structure