  We consider a Borel subalgebra $\fg$ of the general linear algebra and its
subalgebra $\BB$ which is a Borel subalgebra of the special linear algebra,
over arbitrary field. Let $\cL\in\{\fg, \BB\}$. We establish here explicit
realizations of the center $Z(\cL)$ and semi-center $Sz(\cL)$ of the enveloping
algebra, the Poisson center $S(\cL)^{\cL}$ and Poisson semi-center
$S(\cL)^{\cL}_{\si}$ of the symmetric algebra. We describe their structure as
commutative rings and establish isomorphisms $Z(\cL)\cong S(\cL)^{\cL}$,
$Sz(\cL)\cong S(\cL)^{\cL}_{\si}$
