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arXiv · 2505.03015

Rings for Which f.g. Projective Modules Have the FI-extending Property

Peter Danchev·M. Zahiri·S. Zahiri
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Abstract

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}).

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Peter Danchev, M. Zahiri, S. Zahiri. 2025-05-05. Rings for Which f.g. Projective Modules Have the FI-extending Property. https://arxiv.org/abs/2505.03015

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