Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory

About Two Classes of Right Abundant Semigroups

Author HuangHui
Tutor GuoXiaoJiang
School Jiangxi Normal University
Course Basic mathematics
Keywords (Strongly) F-rpp semigroup F-abundant semigroup Abundant semigroup (Left) cancellative monoid Band FR-system IC quasi-adequate semigroup Left regular band R~*-homomorphism Proper cover Left GC-lpp semigroup
CLC O152
Type Master's thesis
Year 2007
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In this thesis, we have studied two classes of right abundant semigroups. This thesis is divided into two chapters and each chapter is an integrated paper.In Chapter 1, we introduce the concept of FR-systems and then establish the structure of the general F-rpp semigroups by using FR-systems. As an application, we obtained the characterizations of F-abundant semigroups. In addition, an example is provided to iIiustrate that strongly F-rpp semigroups form a proper subclass of F-rpp semigroups. This gives a negative answer of an open problem on F-rpp semigroups.Chapter 2 is devoted to IC quasi-adequate semigroups. We prove that each IC quasi-adequate semigroup with left regular band of idempotents has a proper cover. In particular, the structure of proper covers of IC quasi-adequate semigroups with left regular band of idempotents are established. As an application, we obtain some characterizations of proper IC quasi-adequate semigroups with left regular band of idempotents.

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