PRINCIPALLY QUASI-BAER SKEW POWER SERIES MODULES

A module M-R is called principally quasi-Baer (or simply p.q.-Baer) if the annihilator of every cyclic submodule of M-R is generated by an idempotent, as a right ideal. Let be an automorphism of R and M-R be an -compatible module and every countable subset of right semicentral idempotents in R has a generalized countable join or R satisfies the ACC on left annihilator ideals. It is shown that M-R is p.q.-Baer if and only if M[[x]](R[[x; ]]) is p.q.-Baer if and only if M[[x, x(-1)]](R[[x, x)(-1); ]] is p.q.-Baer. As a consequence, we unify and extend nontrivially many of the previously known results such as [11, 15, 20]. Examples to illustrate and delimit the theory are provided.