Some Decision Problems for Inverse Monoid Presentations
Some Decision Problems for Inverse Monoid Presentations
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逆幺半群表示的一些决策问题
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
J. B. Stephen
中科院分区：
文献类型：
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作者：
S. Margolis;J. Meakin;J. B. Stephen
本文综述了作者最近和正在进行的一些工作，目的是发展一种类似于群的生成元和关系的逆么半群的表示理论。我们把逆么半群看作是一类<2，1，0>型代数，并从这个角度研究逆么半群的表示。本文讨论了逆么半群表示的两个基本判定问题：字问题和E-酉性问题。我们发展了与逆么半群表示相关的双根词图的一般结构，并展示了它如何作为研究应用题的基本工具。我们指出了使用这些技巧可以解决字问题的几种情况。我们研究了形式为M=Inv<X|w=1>的逆么半群的E-酉性问题，其中w是X上的自由逆么半群.我们展示了如何利用组合群论的Lyndon图来分析这一问题，并详细地研究了几个例子和特例.
This paper surveys some of the authors’ recent and ongoing work aimed at developing a theory of presentations of inverse monoids analogous to the theory of generators and relations for groups. We regard inverse monoids as a class of algebras of type 〈2,1,0〉 and study presentations of inverse monoids from this point of view. The paper is concerned with two basic decision problems for inverse monoid presentations: the word problem and the E-unitary problem. We develop the general construction of a birooted word graph associated with an inverse monoid presentation and show how it can be used as a basic tool in the study of the word problem. We indicate several cases in which the word problem can be solved using these techniques. We study the E-unitary problem for inverse monoids of the form M=Inv〈X|w=1〉 where w is in the free inverse monoid on X. We show how the Lyndon diagrams of combinatorial group theory may be used to analyze the problem and we study several examples and special cases in detail.