Tam Metin

ABSTRACT
SEMIGROUPS AND THEIR PROPERTIES
Filiz KORKMAZ
Balikesir University, Institute of Science,
Department of Mathematics
(MSc. Thesis / Supervisor: Assoc. Prof. Dr. Ahmet Sinan ÇEVİK)
Balikesir, Turkey-2008
At the beginning of this work, it has been given the special algebraic
structures groups and monoids with their general meanings and presentations, and
then investigated semigroups with their general meanings, presentations and
properties. Moreover, it has been studied in the different part the special type of
semigroups, namely “monogenic semigroups”, that are placed in an important part of
these algebraic structures.
This thesis contains four main chapters.
In the first chapter it has been defined semigroups, investigated emphatically
in the remaining chapters of this thesis, with groups and monoids, after that it has
been studied relationships among them by giving presentations of these three
algebraic structures. It has been also mentioned basic definitions, theorems and
properties (which will be used for the remaining parts of this thesis) about some
different types of semigroups.
In the second chapter the classification of semigroup classes has been
generally investigated by depending on their properties. In addition, by studying
whether or not there is connection between these semigroup classes, it has been
given 2.5.3 Theorem, 2.5.6 Corollary and 2.5.9 Theorem that are proved by myself.
At the end of this chapter there will be seen a proof of an important result, 2.5.11
Theorem, which is about the regularity of semigroups.
Chapter three is the main goal of this thesis. In other words, the monogenic
semigroups have been largely studied in here. To do that, at first, it has been given
definition of an monogenic semigroup, and then has been investigated the elements
of this semigroup. In the remaining parts of this chapter, by mentioning the
properties of monogenic semigroups, it has been studied and then obtained some
results that are about what kind of semigroup classes (that are introduced in the
second chapter) include monogenic semigroups. Also, at the end of this chapter it
has been given presentation of an monogenic semigroup.
The final chapter can be thought as a general summarized the results achieved
whole of this thesis.
KEY WORDS: Semigroups, presentations of semigroups, Green relations,
monogenic semigroups.
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