Affiliation:
1. Laboratoire de Mathématiques Nicolas Oresme UMR 6139, Université de Caen, 14032 Caen, France
Abstract
Define an augmented LD-system, or ALD-system, to be a set equipped with two binary operations, one satisfying the left self-distributivity law x * (y * z) = (x * y) * (x * z) and the other satisfying the mixed laws (x ◦ y) * z = x * (y * z) and x * (y ◦ z) = (x * y) ◦ (x * z). We solve the word problem of the ALD laws, and prove that every element in the parenthesized braid group B• of [2, 3, 5, 6] generates a free ALD-system of rank 1, i.e., that B• is a torsion-free ALD-system.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
4 articles.
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