Global Determinism Of Two Classes Of Semigroups

In this thesis, we will make use of the knowledge of semigroups and universal algebras to investigate the global determinism of the classes of monogenic semigroups and finitely generated free abelian monoids. This thesis is divided into four chapters.The first chapter will be introduction and preliminaries. We introduce the prerequisite knowl-edge and at the same time raise the problem what we will study.In the second chapter we firstly show that the class of all infinite monogenic semigroups satisfies the strong isomorphism property. and so it is globally determined. Secondly, we show that the class of all finite monogenic semigroups is globally determined. but it does not satisfy the strong isomorphism property. According to the two cases, we obtain that the class of all monogenic semigroups is globally determined.In the third chapter we will investigate the finitely generated free abelian monoid. We prove that it is isomorphic to a direct sum of copies of the additive monoid of the set of natural numbers. Basing on the result, we get the class of all finitely generated free abelian monoids is globally determined.The last chapter is the summary of this thesis. According to the contents what we have studied and the key problems what we have solved, we summarize the theoretical significance of this poblem.