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Title: Absolute co-supplement and absolute co-coclosed modules
Authors: Keskin Tütüncü, Derya
Toksoy, Sultan Eylem
Toksoy, Sultan Eylem
Izmir Institute of Technology. Mathematics
Keywords: Supplement submodule
Absolute co-supplement module
General module theory
Issue Date: 2013
Publisher: Hacettepe Üniversitesi
Source: Keskin Tütüncü, D., and Toksoy, S. E. (2013). Absolute co-supplement and absolute co-coclosed modules. Hacettepe Journal of Mathematics and Statistics, 42(1), 67-79.
Abstract: A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.
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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