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- Complements in modular and semimodular latticesPublication . Bordalo, G. H.; Rodrigues, E.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.