The semicenter of the enveloping algebra of a standard borel p-algebra

Motivated by the recent result of [3] that the semi-center of enveloping algebra of a solvable Lie algebra L over a field of prime characteristic is factorial if [L, L] is nilpotent, we will give a description of the semi-center of enveloping algebras of Borel subalgebras over a field of prime characteristic, as a polynomial extension of the center of a better controlled subalgebra. In addition we shall show that the center of the enveloping algebra of a Borel subalgebra need not be factorial.