对自由半群中一类方程解的研究

摘  要

近年来﹐半群代数理论在计算机科学中得到了广泛的应用﹐引起人们的高度重视﹐并成为数学家和计算机科学家深入研究的对象﹐有了迅速的发展。
自由半群是半群的1个很重要的分支。随着科学技术的迅速发展，自由半群在机器自动化及自动操控、语言、码中起到了很重要的作用。本文针对在自由半群中的1类方程a b =c (m,n,p 2)在1定条件下只有平凡解进行了讨论。字是自由半群中的1个核心单元。本文主要从字的长度入手，根据字a和c长度的大小，分为| |>| |、| |=| |、| |<| |3大部分，共分8种情况进行了讨论。

关键字：字；半群；自由半群；长度

ABSTRACT

In recent years, the theories of the semigroup have been applied extensively in computer technology,taking people’s hi-
gh attention ,and have been studied deeply by the mathmatists and computer scientists ,and have developed rapidly.
Free semigroup is a very important branch of the semigroup.With the development of science technology, free semigroup takes a very important role in machine, automate, automatic operation, language,and code . This text discusses that  only has trivial solves under the conditrion that m,n,p 2.The word is a core unit in free semigroup. According to the words length of a and c,the text is divided three parts:|a|>|c|, |a|=|c |, |a|<|c|,and discusses eight kinds of circumstances.

Key words；word;  semigroup;  free semigroup;  length

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