On prime rings whose central closure is finitely generated

The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the extended centroid C, that is, RC=R[c1,…,cn], for some c1,…,cn∈C. In particular, we will show that if there exists a prime ring with zero center whose central closure is simple with 1 and generated by finitely many central elements, then there exists such a ring whose central closure is generated by two central elements.