Mathematical Sciences: Global Structure Theory for ArbitrarySemigroups

本课题研究的是任意无限半群的整体结构理论。应用程序将给予形式语言，无限群论，和决策问题。数学发展将包括以下内容：一般机制，半群间态射的核，展开式，任意半群的素分解定理及其应用。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。

The research on this grant concerns the global structure theory for arbitrary infinite semigroups. Applications will be given to formal languages, infinite group theory, and decision problems. The mathematical development will consist of the following: general machinery, the kernel of a morphism between semigroups, expansions, the prime decomposition theorem for arbitrary semigroups and applications. 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.