Leavıtt yol cebirlerinin ideallerinin sınıflandırılması
Yükleniyor...
Dosyalar
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Düzce Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bir K cismi ve E yönlü çizgesi üzerinde kurulan Leavitt yol cebirleri, 2005 yılında tanımlanmış ve günümüze kadar hem fonksiyonel analiz, hem de halka teorisinin popüler bir araştırma konusu haline gelmiştir. Halka teorisinde, ideallerin sınıflandırılması halkanın yapısı ile ilgili bilgi içerdiği için önemlidir. Leavitt yol cebirlerinin idealleri tek başına ele alınmamış olmakla beraber, pek çok araştırmanın içinde sonuçları mevcuttur. Bu çalışmada konuyla ilgili yayımlanmış makale, kitap ve tezler incelenmiş ve çift yönlü ideal yapısı ile ilgili bilinen tüm sonuçlar derlenerek Türkçe kaynak oluşturulmuştur. Tezde Leavitt yol cebirlerinin, asal, maksimal, ilkel ideal yapıları, dereceli ideal için yapı teoremi, sonlu boyutlu bölümleri incelenmiştir.
Leavitt path algebras that were constructed on a field K and a directed graph E , were first defined in 2005, and have since become a popular research topic in both functional analysis and ring theory. In ring theory, the classification of ideals is important, because it contains information about the structure of the ring. Although the ideals of Leavitt path algebras have not been dealt with alone, their results are in many studies. In this study, published articles, books and theses on the subject were examined, all known results related to two sided ideal structure have been compiled and a source in Turkish has been created. In this thesis, prime, maximal, primitive ideal structures, structure theorem for graded ideals, finite dimensional quotients of Leavitt path algebras have been studied.
Leavitt path algebras that were constructed on a field K and a directed graph E , were first defined in 2005, and have since become a popular research topic in both functional analysis and ring theory. In ring theory, the classification of ideals is important, because it contains information about the structure of the ring. Although the ideals of Leavitt path algebras have not been dealt with alone, their results are in many studies. In this study, published articles, books and theses on the subject were examined, all known results related to two sided ideal structure have been compiled and a source in Turkish has been created. In this thesis, prime, maximal, primitive ideal structures, structure theorem for graded ideals, finite dimensional quotients of Leavitt path algebras have been studied.
Açıklama
YÖK Tez No: 617238
Anahtar Kelimeler
Matematik, Mathematics
