Baer ve quasi-Baer modüller

This study contains the endomorphism rings of retractable modules, Baer, quasi-Baer modules and rings. A module MR is said to be retractable if HomR(M, N) , 0 foreach nonzero submodule N of M. It is shown that if MR is nonsingular and retractable,then EndR(M) = S is a right CS ring if and only if M is CS module. A module MR iscalled (quasi-) Baer if the right annihilator of a (two-sided) left ideal of S = EndR(M)is a direct summand of M. After these definitions, it is shown that a direct summandof a (quasi-) Baer module is also a (quasi-) Baer module and a finitely generated ZmoduleM is a Baer module if and only ifMis semisimple or torsion free. Beside theseit is shown that direct sums of (quasi-) Baer modules are not (quasi-) Baer module.Furthermore, it is shown every free (projective) module over a (quasi-) Baer ring isalways a (quasi-) Baer module. The relation between CS-modules and FI-extendingmodules are exhibited and it is shown that a module MR is (quasi-) Baer and (FI-)K-cononsingular if and only if MR is (FI-) extending and (FI-) K-nonsingular. It is alsoshown that if R is semisimple and artinian if and only if every (right) R-module is Baer.Among other results, the endomorphism ring of a (quasi-) Baer module is a (quasi-)Baer ring, while the converse is not true in general.