We investigate conditions for the existence of relative complements in ordered sets. For relatively complemented ordered sets with 0 we show that each element b ≠ 0 is the least one of the set of all upper bounds of all atoms contained in b.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1018,
author = {Ivan Chajda and Zuzana Mor\'avkov\'a},
title = {Relatively complemented ordered sets},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {207-217},
zbl = {0983.06002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1018}
}
Ivan Chajda; Zuzana Morávková. Relatively complemented ordered sets. Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 207-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1018/
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