Geodesic
Orthorings
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 137-147

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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.
Keywords: ortholattice, generalized ortholattice, sectionally complemented lattice, orthoring, arithmetical variety, weakly regular variety, congruence kernel, ideal term, basis of ideal terms, subtractive term 
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Chajda, Ivan; Länger, Helmut. Orthorings. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 137-147. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a9/