Rings Whose Certain Modules are Dual Self-CS-Baer

In this work, we characterize some rings in terms of dual self-CS-Baer modules (briefly, ds-CS-Baer modules). We prove that any ring R is a left and right artinian serial ring with J² (R) =0 iff R M is ds-CS-Baer for every right R-module M. If R is a commutative ring, then we prove that R is an artinian serial ring iff R is perfect and every R-module is a direct sum of ds-CS-Baer R-modules. Also, we show that R is a right perfect ring iff all countably generated free right R-modules are ds-CS-Baer.