Term substitution induces an associative operation on the free objects of any equational variety. In the case of left distributivity, the construction can be extended to any monogenic structure.
@article{118724,
author = {Patrick Dehornoy},
title = {An associative operation on monogenic left distributive systems},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {36},
year = {1995},
pages = {1-6},
zbl = {0843.20050},
mrnumber = {1334406},
language = {en},
url = {http://dml.mathdoc.fr/item/118724}
}
Dehornoy, Patrick. An associative operation on monogenic left distributive systems. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 1-6. http://gdmltest.u-ga.fr/item/118724/
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