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.
