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We study the relations between the complements of a and b when a is covered by b on finite upper-semimodular lattices and when a < b on modular lattices. We give some results that generalize the well known properties of complements in distibutive lattices. From there, we derive a property of semisimple R-modules. 1 – Introduction In this paper we will only… (More)

- Pedro Resende, Elias Rodrigues
- Applied Categorical Structures
- 2010

We revisit sheaves on locales by placing them in the context of the theory of Hilbert quantale modules. The local homeomorphisms p : X → B are identified with the locales X that are Hilbert B-modules equipped with a natural notion of basis. These modules form a full subcategory B-HMB of the category of Hilbert B-modules where all the homomorphisms are… (More)

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