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
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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 .are absolute co-coclosed (absolute co-supplement) are precisely determined.
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Temel Bulgular & Veri:We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective.
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Sonuç & Katkı: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
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Absolute co-supplement (co-coclosed) module · Supplement (coclosed) submodule · 2000 AMS Classification: Primary 16 D 10. Secondary 06 C 05
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 .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
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