Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5798
Title: Small supplements, weak supplements and proper classes
Authors: Alizade, Rafail
Büyükaşık, Engin
Durğun, Yılmaz
Keywords: Small module
General module theory
Homological functors on modules
Proper class of short exact sequences
Commutative rings
Issue Date: 2016
Publisher: Hacettepe Üniversitesi
Source: Alizade, R., Büyükaşık, E., and Durğun, Y. (2016). Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics, 45(3), 649-661. doi:10.15672/HJMS.20164512507
Abstract: Let SS denote the class of short exact sequences E:0 → Af→ 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 such that 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 class SS coincides with the smallest proper class containing the class of short exact sequences determined by weak supplement submodules. The homological objects, such as, SS-projective and SScoinjective modules are investigated. In order to describe the class SS, we investigate small supplemented modules, i.e. the modules each of whose submodule has a small supplement. Besides proving some closure properties of small supplemented modules, we also give a complete characterization of these modules over Dedekind domains.
URI: http://hdl.handle.net/11147/5798
https://search.trdizin.gov.tr/yayin/detay/209056
ISSN: 1303-5010
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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