Decreasing chains without lower bounds in Rudin-Frolík order for regulars

The aim of this paper is to prove that for there exist a chain in the Rudin-Frolík order of $\beta \kappa \setminus \kappa$ of length $\mu$ with $\kappa ⩽\mu ⩽2^{\kappa }$ for regular $\kappa >\omega$ without a lower bound.