A generalization of semiperfect modules
A module $M$ is called radical semiperfect, if $\frac MN$ has a projective cover whenever $\mathrm{R}\mathrm{a}\mathrm{d}(M) \subseteq N \subseteq M$. We study various properties of these modules. It is proved that every left $R$-module is radical semiperfect if and only if $R$ is left perfect. Mo...
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| Datum: | 2017 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1679 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | A module $M$ is called radical semiperfect, if $\frac MN$ has a projective cover whenever $\mathrm{R}\mathrm{a}\mathrm{d}(M) \subseteq N \subseteq M$. We study various properties of these modules. It is proved that every left $R$-module is radical semiperfect if and only if $R$ is left perfect.
Moreover, radical lifting modules are defined as a generalization of lifting modules. |
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