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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

On a new variation of injective modules

Ali Pancar0000-0003-3870-9210
Burcu Nişancı Türkmen0000-0001-7900-0529
Celil Nebiyev0000-0002-7992-7225
Ergül Türkmen0000-0002-7082-1176
Sayfa
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Yayın Tarihi
2019-02-01
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We also prove that, if a ring R is a local Dedekind domain, an R-module M is a GE-module if and only if M≅(R^{∗})ⁿ⊕K⊕N, where R^{∗} is the completion of R, K is injective and N is a bounded module.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we provide various properties of GE and GEE-modules, a new variation of injective modules.
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Temel Bulgular & Veri:We call M a GE-module if it has a g-supplement in every extension N and, we call also M a GEE-module if it has ample g-supplements in every extension N.
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Sonuç & Katkı:We also prove that, if a ring R is a local Dedekind domain, an R-module M is a GE-module if and only if M≅(R^{∗})ⁿ⊕K⊕N, where R^{∗} is the completion of R, K is injective and N is a bounded module.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:g-supplement · GE-module

Abstract

In this paper, we provide various properties of GE and GEE-modules, a new variation of injective modules. We call M a GE-module if it has a g-supplement in every extension N and, we call also M a GEE-module if it has ample g-supplements in every extension N. In particular, we prove that every semisimple module is a GE-module. We show that a module M is a GEE-module if and only if every submodule is a GE-module. We study the structure of GE and GEE-modules over Dedekind domains. Over Dedekind domains the class of GE-modules lies between WS-coinjective modules and Zöschinger's modules with the property (E). We also prove that, if a ring R is a local Dedekind domain, an R-module M is a GE-module if and only if M≅(R^{∗})ⁿ⊕K⊕N, where R^{∗} is the completion of R, K is injective and N is a bounded module.

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Bu Makaleye Atıf Yap

Pancar, A., Türkmen, B. N., Nebiyev, C., Türkmen, E. (2019). On a new variation of injective modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.464103

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Kaynakça (15)

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