Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1081,
author = {Ivan Chajda and Helmut L\"anger},
title = {Orthorings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {24},
year = {2004},
pages = {137-147},
zbl = {1080.16053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1081}
}
Ivan Chajda; Helmut Länger. Orthorings. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 137-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1081/
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