Birkenmeier, Gary F.Kara, YelizTercan, Adnan2024-07-292024-07-292020-03-030092-7872https://doi.org/10.1080/00927872.2019.1677690https://www.tandfonline.com/doi/full/10.1080/00927872.2019.1677690https://hdl.handle.net/11452/43509Let N be a submodule of a right R-module M-R, and Then N is said to be projection invariant in M, denoted by if for all We call M-R ?-endo Baer, denoted ?-e.Baer, if for each there exists such that where denotes the left annihilator of N in H. We show that this class of modules lies strictly between the classes of Baer and quasi-Baer modules introduced in 2004 by Rizvi and Roman. Several structural properties are developed. In contrast to the Baer modules of Rizvi and Roman, the free modules of a Baer ring are ?-e.Baer. Moreover, (co-) nonsingularity conditions are introduced which enable us to extend the Chatters-Khuri result (connecting the extending and Baer conditions in a ring) to modules. We provide examples to illustrate and delimit our results.eninfo:eu-repo/semantics/closedAccessDirect sumsInvariantSubmodulesRingsBaer moduleEndomorphism ringsProjection invariant submoduleQuasi-baer modulePi-extending modulePi-e.Baer moduleMathematicsArticle0004942278000011132114948310.1080/00927872.2019.1677690