Titlebook: Semilocal Categories and Modules with Semilocal Endomorphism Rings; Alberto Facchini Book 2019 Springer Nature Switzerland AG 2019 semiloc

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Semilocal Categories and Their Maximal Ideals,f . is the unique ideal of the category . properly containing .. Obviously, if all objects of . are zero objects, maximal ideals do not exist in .. In this section, we will characterize maximal ideals in preadditive categories.

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Semilocal Rings,In this section, we recall the notions of Goldie dimension of a modular lattice and Goldie dimension of a module. In fact, the notion of Goldie dimension of a module concerns the lattice L(M) of all submodules of M, which is a modular lattice.

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Additive Categories,The aim of this chapter is to point out some aspects of additive categories that usually are not sufficiently stressed in a first course in category theory.

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,Auslander–Bridger Transpose, Auslander–Bridger Modules,The idea of the Auslander–Bridger transpose is the following. We have a finitely presented right R-module MR, defined by m generators and s relations say. Thus MR has a free presentation

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