Mathematical Sciences: Algorithmic and Computational Methodsin Algebra

本文主要研究群、半群、逆半群和结合代数理论中的算法问题。还将考虑自动机、变种和伪变种的相关问题。要考虑的算法问题包括非周期半群变异的词问题、有限基结合代数变异的词问题、逆半群的表示和变异的词问题。其他要考虑的问题包括通过有限逆模群有限生成的自由群的子群的算法分类，有限群类的Rhodes问题和有限逆自动机到各种伪群的扩展问题。这项研究是在半群领域。半群是抽象数学结构中最简单的一种，它由一组对其进行结合运算的集合组成。我们将研究这些非常一般的物体的结构。应用将给予数学和计算机科学的各个领域。

This research is concerned with a study of algorithmic problems in the theories of groups, semigroups, inverse semigroups and associative algebras. Related problems about automata, varieties and pseudo-varieties will also be considered. Algorithmic problems to be considered include the word problem for non-periodic semigroup varieties, for finitely based varieties of associative algebras, for presentations and varieties of inverse semigroups. Other problems to be considered include the algorithmic classification of finitely generated subgroups of free groups via finite inverse monoids, the Rhodes problem for the class of finite groups and the extension problem for finite inverse automata to various pseudo-varieties of groups. This research is in the area of semigroups. A semigroup is one of the simplest of the abstract mathematical structures, consisting of a set with one associative operation on it. The structure of these very general objects will be investigated. Applications will be given to various areas of mathematics and computer science.