The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm

Central European Journal of Mathematics Pub Date : 2013-10-08 DOI:10.2478/s11533-013-0290-0

R. Laver, Sheila K. Miller

引用次数: 9

Abstract

The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity of the iterated left division ordering

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自由单生成左分配代数:除法算法的基础和简化证明

左分配律是a·(b·c) = (a·b)·(a·c)。左分配代数已被经典地用于研究结和辫，最近自由的左分配代数已与集合论中的大基数公理联系起来研究。本文综述了在生成子a上的自由左分配代数的结果，并给出了a中项的范式存在性的一个新的简化证明，包括:a的合流性，a的迭代左除序

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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