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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2505.03015 |
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| _version_ | 1866913822394023936 |
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| author | Danchev, Peter Zahiri, M. Zahiri, S. |
| author_facet | Danchev, Peter Zahiri, M. Zahiri, S. |
| contents | A right $R$-module $M$ is said to be {\it FI-extending} if any fully invariant submodule of $M$ is essential in a direct summand of $M$. In this short note we prove that if $R$ has ACC on the right annihilators, then $R_R$ is FI-extending if, and only if, every f.g. projective module is too FI-extending. This is an affirmative answer to the question raised by Birkenmeier-Park-Rizvi in Commun. Algebra on 2002 (see \cite{2}). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rings for Which f.g. Projective Modules Have the FI-extending Property Danchev, Peter Zahiri, M. Zahiri, S. Rings and Algebras Representation Theory 16D15, 16D40, 16D70 A right $R$-module $M$ is said to be {\it FI-extending} if any fully invariant submodule of $M$ is essential in a direct summand of $M$. In this short note we prove that if $R$ has ACC on the right annihilators, then $R_R$ is FI-extending if, and only if, every f.g. projective module is too FI-extending. This is an affirmative answer to the question raised by Birkenmeier-Park-Rizvi in Commun. Algebra on 2002 (see \cite{2}). |
| title | Rings for Which f.g. Projective Modules Have the FI-extending Property |
| topic | Rings and Algebras Representation Theory 16D15, 16D40, 16D70 |
| url | https://arxiv.org/abs/2505.03015 |