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Absolute Co-Supplement and Absolute Co-Coclosed Modules
(Hacettepe Üniversitesi, 2013) Tütüncü, Derya Keskin; Toksoy, Sultan Eylem
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.
Citation - WoS: 8
Citation - Scopus: 8
Modules Whose Maximal Submodules Are Supplements
(Hacettepe Üniversitesi, 2010) Büyükaşık, Engin; Pusat, Dilek
We study modules whose maximal submodules are supplements (direct summands). For a locally projective module, we prove that every maximal submodule is a direct summand if and only if it is semisimple and projective. We give a complete characterization of the modules whose maximal submodules are supplements over Dedekind domains.

TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection