BRAID-GROUPS AND LEFT DISTRIBUTIVE OPERATIONS

The decidability of the word problem for the free left distributive law is proved by introducing a structure group which describes the underlying identities. This group is closely connected with Artin's braid group B-infinity. Braid colourings associated with free left distributive structures are used to show the existence of a unique ordering on the braids which is compatible with left translation and such that every generator sigma(i) is preponderant over all sigma(k); with k > i. This ordering is a linear ordering.