Rings for which f.g. projective modules have the FI-extending property
Volume 180 / 2026
Colloquium Mathematicum 180 (2026), 31-35
MSC: Primary 16D40; Secondary 16D70
DOI: 10.4064/cm9655-10-2025
Published online: 13 February 2026
Abstract
A right $R$-module $M$ over a ring $R$ is said to be FI-extending if any fully invariant submodule of $M$ is essential in a direct summand of $M$. 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 over $R$ is FI-extending. This is an affirmative answer to the question raised by Birkenmeier–Park–Rizvi [Comm. Algebra 30 (2002), 1833–1852].
