  Let $R$ be a ring. It is proved that an $R$-module $M$ is Baer (resp. dual
Baer) if and only if every exact sequence $0\rightarrow X\rightarrow
M\rightarrow Y\rightarrow 0$ with $Y\in$ Cog$(M_R)$ (resp. $X\in$ Gen$(M_R)$)
splits. This shows that being (dual) Baer is a Morita invariant property. As
more applications, the Baer condition for the $R$-module $M^+ $ = Hom$_{\Bbb
Z}(M,{\Bbb Q}/{\Bbb Z})$ is investigated and shown that $R$ is a von Neumann
regular ring, if $R^+$ is a Baer $R$-module. Baer modules with (weak) chain
conditions are studied and determined when a Baer (resp. dual baer) module
  is a direct sum of mutually orthogonal prime (resp. co-prime) modules.
Finitely generated dual Baer modules over commutative rings are studeid
