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

2025/05/05 by Peter Danchev, Danchev, Peter, Masoome Zahiri +3
Mathematics · #16D15 #16D40 #16D70 #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.03015

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \cite2).

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