Pseudo-BCH cebirleri üzerine
Yükleniyor...
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ege Üniversitesi, Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezde cebirsel bir yapı olan pseudo-BCH cebirlerinin tanım ve temel özellikleri verilerek, pseudo-BCH cebirlerinde merkez, dallar ve idealler incelenmiştir. Birinci bölümde, tezin konusu tanıtılmış, konunun çalışılma amacı ve süreci özetlenmiştir. İkinci bölümde, Hu ve Li’nin 1983 yılında yayınlanan, Dudek ve Jun’un 2008 de yayınlanan, Dymek’in 2011 ve 2012 de yayınlanan makaleleri temel alınarak sonraki bölümlerin kolay anla¸sılması için gerekli bazı tanım ve önermeler verilmiştir. Ayrıca BCH-cebirleri ve BCI-cebirleri arasındaki ilişkiye ve pseudo-BCI cebirleri ve pseudo-BCK cebirleri arasındaki ilişkiye değinilmiştir. Üçüncü bölümde,Walendziak’ın 2015 ve 2016 yılında yayınlanan makaleleri temel alınarak pseudo-BCH cebirlerinin tanımı ve temel özellikleri verilmiştir. Pseudo-BCI cebirleri ve pseudo-BCH cebirleri arasındaki fark incelenmiştir. Ayrıca "Bir pseudo-BCH cebri ne zaman bir grup yapısı gösterir?" sorusu cevap bulmuştur. Dördüncü bölümde, Walendziak’ın 2015, 2016 ve 2017 de yayınlanan makaleleri temel alınarak pseudo-BCH cebirlerinde, merkez ve dallar olmak üzere pseudo-BCH cebirleri iki alt başlıkta detaylandırılmıştır. Bu bölümde bu yapıların birbirleriyle olan ilişkilerine değinilmiştir. Beşinci bölümde, Walendziak’ın 2015 ve 2016 yılında yayınlanan makaleleri temel alınarak pseudo-BCH ideali kavramı tanıtılmış ve genel özellikleri incelenmiştir. Ayrıca kapalı, güçlü ve horizontal idealler olmak üzere pseudo-BCH cebirleri üç alt başlıkta detaylandırılmıştır. Altıncı bölümde, bu tez çalışmasında elde edilen sonuçlar ve devamında yapılacak olan çalışmalar bulunmaktadır.
In this thesis, definition and basic properties of BCH-algebras, center, branches and ideals of pseudo-BCH algebras are investigated. In the first section, the subject of the thesis is introduced, the goal of working on this area and the development process of the subject are summarized. In the second section, by primiraly considering the paper of Hu and Li which is published in 1983 , the paper of Dudek and Jun which is published in 2008, the paper of Dymek which is published in 2011 and 2012, some definitions and propositions are given which are necessary for easy understanding of next sections. The connection between BCH-algebras and BCI-algebras is given and also connection between pseudo-BCH-algebras and pseudo-BCI-algebras is given. In the third section, by primiraly considering the paper of Walendziak which is published in 2015 and 2016, definition and some basic properties of pseudo-BCH algebras are given and the difference between pseudo-BCI algebras and pseudo-BCH algebras is investigated. Also, the question which is "When does a pseudo-BCH algebras turn into a group?" is answered. In the forth section, by primarily considering the paper of Walendziak which is published in 2015, 2016 and 2017 two subtitles which are center and branches of pseudo-BCH algebras are investigated. In this section, the relations of these structures with each other are mentioned. In the fifth section, by primiraly considering the paper of Walendziak which is published in 2015 and 2016 definition and some basic properties of pseudo-BCH ideals are introduced. Also, three subtitles which are closed, strong and horizontal ideals of pseudo-BCH algebras are investigated. In the sixth section, the conclusion of this work and the future work are given.
In this thesis, definition and basic properties of BCH-algebras, center, branches and ideals of pseudo-BCH algebras are investigated. In the first section, the subject of the thesis is introduced, the goal of working on this area and the development process of the subject are summarized. In the second section, by primiraly considering the paper of Hu and Li which is published in 1983 , the paper of Dudek and Jun which is published in 2008, the paper of Dymek which is published in 2011 and 2012, some definitions and propositions are given which are necessary for easy understanding of next sections. The connection between BCH-algebras and BCI-algebras is given and also connection between pseudo-BCH-algebras and pseudo-BCI-algebras is given. In the third section, by primiraly considering the paper of Walendziak which is published in 2015 and 2016, definition and some basic properties of pseudo-BCH algebras are given and the difference between pseudo-BCI algebras and pseudo-BCH algebras is investigated. Also, the question which is "When does a pseudo-BCH algebras turn into a group?" is answered. In the forth section, by primarily considering the paper of Walendziak which is published in 2015, 2016 and 2017 two subtitles which are center and branches of pseudo-BCH algebras are investigated. In this section, the relations of these structures with each other are mentioned. In the fifth section, by primiraly considering the paper of Walendziak which is published in 2015 and 2016 definition and some basic properties of pseudo-BCH ideals are introduced. Also, three subtitles which are closed, strong and horizontal ideals of pseudo-BCH algebras are investigated. In the sixth section, the conclusion of this work and the future work are given.
Açıklama
Anahtar Kelimeler
BCH-Cebirleri, Pseudo-BCI Cebirleri, Pseudo-BCK Cebirleri, Pseudo-BCH Cebirleri, BCH-Algebras, Pseudo-BCI Algebras, Pseudo-BCK Algebras, Pseudo-BCH Algebras
