Small supplements, weak supplements and proper classes

DUR?GUN, Yılmaz; BÜYÜKAŞIK, Engin; ALİZADE, Rafail

Small supplements, weak supplements and proper classes

Rafail ALİZADE, (Yaşar Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İzmir, Türkiye)

Engin BÜYÜKAŞIK, (İzmir Yüksek Teknoloji Enstitüsü, Matematik Bölümü, İzmir, Türkiye)

Yılmaz DUR?GUN (Bitlis Eren Üniversitesi, Matematik Bölümü, Bitlis, Türkiye)

Hacettepe Journal of Mathematics and Statistics

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Yıl: 2016 Cilt: 45 Sayı: 3 Sayfa Aralığı: 649 - 661 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Small supplements, weak supplements and proper classes

Öz:

Let SS denote the class of short exact sequences E :0 -> A-> B ->C -> 0 of R-modules and R-module homomorphisms such that f (A)has a small supplement in B i.e. there exists a submodule K of M suchthat f (A) + K = B and f (A) ? K is a small module. It is shown that,SS is a proper class over left hereditary rings. Moreover, in this case,the proper classSS coincides with the smallest proper class containing the class of short exact sequences determined by weak supplementsubmodules. The homological objects, such as,SS-projective and SScoinjective modules are investigated. In order to describe the classSS,we investigate small supplemented modules, i.e. the modules each ofwhose submodule has a small supplement. Besides proving some closure properties of small supplemented modules, we also give a completecharacterization of these modules over Dedekind domains

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	ALİZADE R, BÜYÜKAŞIK E, DUR?GUN Y (2016). Small supplements, weak supplements and proper classes. , 649 - 661.
Chicago	ALİZADE Rafail,BÜYÜKAŞIK Engin,DUR?GUN Yılmaz Small supplements, weak supplements and proper classes. (2016): 649 - 661.
MLA	ALİZADE Rafail,BÜYÜKAŞIK Engin,DUR?GUN Yılmaz Small supplements, weak supplements and proper classes. , 2016, ss.649 - 661.
AMA	ALİZADE R,BÜYÜKAŞIK E,DUR?GUN Y Small supplements, weak supplements and proper classes. . 2016; 649 - 661.
Vancouver	ALİZADE R,BÜYÜKAŞIK E,DUR?GUN Y Small supplements, weak supplements and proper classes. . 2016; 649 - 661.
IEEE	ALİZADE R,BÜYÜKAŞIK E,DUR?GUN Y "Small supplements, weak supplements and proper classes." , ss.649 - 661, 2016.
ISNAD	ALİZADE, Rafail vd. "Small supplements, weak supplements and proper classes". (2016), 649-661.

APA	ALİZADE R, BÜYÜKAŞIK E, DUR?GUN Y (2016). Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics, 45(3), 649 - 661.
Chicago	ALİZADE Rafail,BÜYÜKAŞIK Engin,DUR?GUN Yılmaz Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics 45, no.3 (2016): 649 - 661.
MLA	ALİZADE Rafail,BÜYÜKAŞIK Engin,DUR?GUN Yılmaz Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics, vol.45, no.3, 2016, ss.649 - 661.
AMA	ALİZADE R,BÜYÜKAŞIK E,DUR?GUN Y Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics. 2016; 45(3): 649 - 661.
Vancouver	ALİZADE R,BÜYÜKAŞIK E,DUR?GUN Y Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics. 2016; 45(3): 649 - 661.
IEEE	ALİZADE R,BÜYÜKAŞIK E,DUR?GUN Y "Small supplements, weak supplements and proper classes." Hacettepe Journal of Mathematics and Statistics, 45, ss.649 - 661, 2016.
ISNAD	ALİZADE, Rafail vd. "Small supplements, weak supplements and proper classes". Hacettepe Journal of Mathematics and Statistics 45/3 (2016), 649-661.