Extensions of Baer and Principally Projective Modules

In this note, we investigate extensions of Baer and principally projective modules. Let R be an arbitrary ring with identity and M a right R-module. For an abelian module M, we show that M is Baer insert ignore into journalissuearticles values(resp. principally projective); if and only if the polynomial extension of M is Baer insert ignore into journalissuearticles values(resp. principally projective); if and only if the power series extension of M is Baer insert ignore into journalissuearticles values(resp. principally projective); if and only if the Laurent polynomial extension of M is Baer insert ignore into journalissuearticles values(resp. principally projective); if and only if the Laurent power series extension of M is Baer insert ignore into journalissuearticles values(resp. principally projective);.