WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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Conference Object Citation - WoS: 7On dual baer modules(American Mathematical Society, 2014) Tütüncü, Derya Keskin; Tütüncü, Derya Keskin; Smith, Patrick F.; Toksoy, Sultan Eylem; Toksoy, Sultan Eylem; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this note we prove that any ring R is right cosemihereditary if and only if every finitely cogenerated injective right R-module is d-Rickart. Let M be a module. We prove that if M is a dual Baer module with the (D-2) condition, then S = End(R)(M) is a right self-injective ring. We also prove that if M = M-1 circle plus M-2 with M-2 semisimple, then M is dual Baer if and only if M-1 is dual Baer and every simple non-direct summand of M-1 does not embed in M-2.Article Absolute Co-Supplement and Absolute Co-Coclosed Modules(Hacettepe Üniversitesi, 2013) Tütüncü, Derya Keskin; Toksoy, Sultan Eylem; Tütüncü, Derya Keskin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyA 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.