Conditions forcing the existence of relative complements in lattices and posets

Abstract It is elementary and well known that if an element x of a bounded modular lattice L $ \mathbf L has complement in then relative every interval [ , b ] containing . We show the relatively strong assumption modularity can be replaced by weaker one formulated language so-called triples. further that, general, we need not suppose By introducing concept triples posets, extend our results obtained for lattices to posets. should remarked notion introduced also posets are bounded.