A Generalization of Lifting Modules
We introduce the notion of $I$ -lifting modules as a proper generalization of the notion of lifting modules and present some properties of this class of modules. It is shown that if $M$ is an $I$ -lifting direct projective module, then $S/▽$ is regular and $▽ = \text{Jac} S$, where $S$ is the ring o...
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| Datum: | 2014 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2239 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We introduce the notion of $I$ -lifting modules as a proper generalization of the notion of lifting modules and present some properties of this class of modules. It is shown that if $M$ is an $I$ -lifting direct projective module, then $S/▽$ is regular and $▽ = \text{Jac} S$, where $S$ is the ring of all $R$-endomorphisms of $M$ and $▽ = \{ϕ ∈ S | Im ϕ ≪ M\}$. Moreover, we prove that if $M$ is a projective $I$ -lifting module, then $M$ is a direct sum of cyclic modules. The connections between $I$ -lifting modules and dual Rickart modules are presented. |
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